UCRL-16231 UNIVERSITY OF CALIFORNIA AEC …TO: FROM: Subject: UNIVERSITY OF CALIFORNIA Lawrence Radiation Laboratory Berkeley, California AEC Contract No. W-7405-eng-48 September 24,

UCRL-16231

UNIVERSITY OF CALIFORNIA

Lawrence Radiation LaboratoryBerkeley, California

AEC Contract No. W-7405-eng-48

SEMICONDUCTOR DETECTORS

forNUCLEAR SPECTROMETRY*

Fred S. Goulding

July 30, 1965

*Lectures to be given at Herceg-Novi, Yugoslavia, August, 1965.

TO:

FROM:

Subject:

UNIVERSITY OF CALIFORNIALawrence Radiation Laboratory

Berkeley, California

AEC Contract No. W-7405-eng-48

September 24, 1965

ERRATA

All recipients of UCRL-16231

Technical Information Division

UCRL-16231, "Semiconductor Detectors for NuclearSpectrometry," by Fred S. Goulding, dated July 30, 1965.

Please make the following corrections on subject report.

Figures 3-2 and 3-3 should be replaced by the attached figures.

Page 91, line 12 should be changed to read"The Fano factor established by these measurements is.30 ± 0.03 which is entirely consistent with the approximatevalue of 0.32 derived from Van Roosbroeck’s curves."

UNIVERSITY OF CALIFORNIADepartment of PhysicsBERKELEY 4, CALIFORNIA

RETURN POSTAGE GUARANTEED

-ii- UCRL-16231

SEMICONDUCTOR DETECTORS FOR NUCLEAR SPECTROMETRY

Table of Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Properties of Solid-State Detector Materials . . . . . . . . . . . 4

1.3 Semiconductor Properties of Silicon and Germanium . . . . . . . . . 7

1.3.1 Intrinsic Material Properties . . . . . . . . . . . . . . . 7

1.3.2 Extrinsic Material General Properties . . . . . . . . . . . 10

1.3.3 More Detailed Behavior of Carriers in Extrinsic Material . . 13

1.4 Junctions in Semiconductors . . . . . . . . . . . . . . . . . . . . 17

1.4.1 Descriptive Junction Theory . . . . . . . . . . . . . . . . 17

1.4.2 Reverse Biased Junction . . . . . . . . . . . . . . . . . . 19

1.4.3 Junction Capacitance . . . . . . . . . . . . . . . .. . . . 20

1.4.4 Junction Leakage Currents . . . . . . . . . . . . . . . . . 21

1.4.5 P-I-N Junctions . . . . . . . . . . . . . . . . . . . . . . 24

1.4.6 Metal to Semiconductor Surface Barrier Junctions . . . . . . 25

Lecture 1. Figure Captions . . . . . . . . . . . . . . . . . . . . . . 29

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

.

.

2.2 Discussion of Purity of Semiconductor Materials . . . . . . . . . . 40

2.3 Diffused Silicon Detectors . . . . . . . . . . . . . . . . . . . 41

2.3.1 Elementary Considerations . . . . . . . . . . . . . . . . . 41

2.3.2 Surface Properties . . . . . . . . . . . . . . . . . . . . . 45

2.3.3 Preparation of Diffused Detectors . . . . . . . . . . . . . 49

-iii- UCRL-16231

2.4 Compensation by Lithium Drifting . . . . . . . . . . . . . . . . . 53

2.4.1 General Principles . . . . . . . . . . . . . . . . . . . . 53

2.4.2 Secondary Effects in Lithium Drifting . . . . . . . . . . . 57

2.4.3 Surface Effects in Lithium-Drifted Devices . . . . . . . . 60

2.4.4 Preparation of Lithium-Drifted Silicon Detectors . . . . . 60

2.4.5 Preparation of Lithium-Drifted Germanium Detectors . . . . 64

2.5 Detectors Not Employing Junctions . . . . . . . . . . . . . . . . 67

2.6 Making The Choice Between Detector Types . . . . . . . . . . . . . 69

Lecture 2. Figure Captions . . . . . . . . . . . . . . . . . . . . . 72

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2 Statistical Spread in the Detector Signal . . . . . . . . . . . . 88

3.3 Electrical Noise Sources . . . . . . . . . . . . . . . . . . . . . 91

3.4 Effect of Amplifier Shaping Networks . . . . . . . . . . . . . . . 95

3.5 Vacuum Tubes as the Input Amplifying Device . . . . . . . . . . . 103

3.6 Alternative Lou Noise Amplifying Elements . . . . . . . . . . . . 107

3.7 Additional Sources of Signal Amplitude Spread . . . . . . . . . . 113

3.7.1 Noise Contribution of Main Amplifier . . . . . . . . . . . 113

3.7.2 Gain Drifts . . . . . . . . . . . . . . . . . . . . . . . . 114

3.7.3 High Counting Rates . . . . . . . . . . . . . . . . . . . . 114

3.7.4 Finite Detector Pulse Rise Time . . . . . . . . . . . . . . 115

Lecture 3. Figure Captions . . . . . . . . . . . . . . . . . . . . . 118

4.1 Detector Pulse Shape . . . . . . . . . . . . . . . . . . . . . . . 138

4.1.1 Pulse Shape Due to a Single Hole-Electron Pair in P-I-N Detector . . . . . . . . . . . . . . . . . . . . . . 139

4.1.2 Pulse Shape Due to a Single Hole-Electron Pair in ap-n Junction Detector . . . . . . . . . . . . . . . . . . . 141

4.1.3 Pulse Shape Distribution for Gamma-rays in GermaniumP-I-N Detectors at 77°K . . . . . . . . . . . . . . . . . . 146

4.1.4 Pulse Shape Distribution for Protons and Alpha-ParticlesStopping in a Lithium-Drifted Silicon Detector . . . . . . 149

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4.2 Radiation Damage in Detectors . . . . . . . . . . . . . . . . . . . 150

4.2.1 Damage Mechanism . . . . . . . . . . . . . . . . . . . . . . 150

4.2.2 Consequences of Damage in p-n Junction Detectors . . . . . . 153

4.2.3 Consequences of Damage in Lithium-Drifted Silicon Detectors 156

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Lecture 4. Figure Captions . . . . . . . . . . . . . . . . . . . . . . 160

References . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . 169

Table 1.1 Some Properties of Silicon and Germanium . . . . . . . . 27

Table 1.2 Impurities in Ge & Si . . . . . . . . . . . . . . . . . 28

Table 3.1 Noise Integral and Peak Response of Several Networks . . 116

Table 3.2 Input Pulse Shape Dependancc of Several Shaping Networks 117

Fig. 1.1 Unit Cell of Single Crystal Si and Ge . . . . . . . . . . . 30

Fig. 1.2 Variation of Mobility with Temperature in Pure Samples . . . 31

Fig. 1.3 Resistivity - Impurity Concentration for Si . . . . . . . . 32

Fig. 1.4 Resistivity - Impurity Concentration for Ge . . . . . . . . 33

Fig. 1.5 Effect of Impurities on Mobility . . . . . . . . . . . . . . 34

Fig. 1.6 Resistivity Temperature Relation for an Extrinsic Silicon

Fig. 1.7 Diagram of a P-N Junction in Equilibrium . . . . . . . . . . 36

Fig. 1.8 A Reverse Biased P-N Junction . . . . . . . . . . . . . . . 37

Fig. 1.9 An N+ PP+ Punch-Through Diode . . . . . . . . . . . . . . . 38

Fig. 2.1 Depletion Layer Thickness Curves for N and P-Type Silicon . 73

Fig. 2.2 Illustration of Charge Injection at Rear Contact . . . . . . 74

Fig. 2.3 Models of Surface Layers at Junction Edge . . . . . . . . . 75

Fig. 2.4 Effect of Ambients on Leakage Current of a Junction . . . . 76

Fig. 2.5 Guard-Ring Structure . . . . . . . . . . . . . . . . . . . . 77

Fig. 2.6 Typical Leakage Curve for Guard-Ring Detector . . . . . . . 78

Fig. 2.7 Steps in Preparing a Planar Junction Device . . . . . . . . 79

Fig. 2.8 Distribution of Lithium at States of Lithium Drift . . . . . 80

Fig. 2.9 Drifted Region Thickness - Time Relationship for Silicon . . 81

Fig. 2.10 Drifted Region Thickness - Time Relationship for Germanium . 82

Fig. 2.11 Illustration of Silicon Wafer Prior to Drifting . . . . . . 83

Fig. 2.12 Cutaway View of Lithium-Drifted Silicon Detector . . . . . . 84

Fig. 2.13 Germanium-Lithium-Drift Unit . . . . . . . . . . . . . . . . 85

Fig. 2.14 Diagram of Germanium Detector Holder and Cryostat . . . . . 86

-v- UCRL-16231

LIST OF FIGURES

Sample . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Fig. 3.1 Diagrammatic Representation of Energy Loss Process . . . . 119

Fig. 3.2 Calculated Yield and Fano Factor . . . . . . . . . . . . . 120

Fig. 3.3 Resolution-Energy Relationship Data for Germanium . . . . . 121

Fig. 3.4 Typical Electronics for Spectroscopy . . . . . . . . . . . 122

Fig. 3.5 Simplified Input Equivalent Circuits . . . . . . . . . . . 123

Fig. 3.6 Typical Shaping Networks and Their Frequency Response . . . 124

Fig. 3.7 Pulse Response of Several Networks (Unit Function Input) . 125

Fig. 3.8 EC-1000 Preamplifer . . . . . . . . . . . . . . . . . . . . 126

Fig. 3.9 Noise Performance Curves for EC-1000 Preamplifer . . . . . 127

Fig. 3.10 EC-1000 Preamplifer: Effect of Double Integrator . . . . . 128

Fig. 3.11 EC-1000 Preamplifer . . . . . . . . . . . . . . . . . . . . 129

Fig. 3.12 EC-1000 Preamplifer Rise Time Curves . . . . . . . . . . . 130

Fig. 3.13 Bulk Field-Effect Transistor (N-Channel Type Illustrated) . 131

Fig. 3.14 General Purpose Field Effect Transistor Preamplifer . . . . 132

Fig. 3.15 Predicted Noise Behavior of Field-Effect Transistor at 300°K 133

Fig. 3.16 Predicted Noise Behavior of Field Effect Transistor at 77°K 134

Fig. 3.17 Circuit for Low Temperature Tests on Field-Effect Transistors 135

Fig. 3.18 Noise Performance of TIS-05 Field Effect Transistor . . . . 136

Fig. 3.19 Noise Performance of Amelco 2N3458 Field-Effect Transistor. 137

Fig. 4.1 Collection of Hole-Electron Pair in a p-i-n Detecotr . . . 161

Fig. 4.2 Signal Output Due to a Single Electron Hole Pair in a

Fig. 4.3 Collection of Hole-Electron Pair in a P-N Junction . . . . 163

Fig. 4.4 Signal Output due to a Single Electron-Hole Pair in a

Fig. 4.5 Expected Range of Pulse Shapes from p-i-n Germanium

Fig. 4.6 Distribution in Triggering Delays of a Discriminator set to

Fig. 4.7 Detector Pulse Shape for Alphas . . . . . . . . . . . . . . 167

Fig. 4.8 Frenkel Defect Production by Alphas and Protons (Silicon) . 168

-vi- UCRL-16231

p-i-n Detector . . . . . . . . . . . . . . . . . . . . . . 162

P-N Junction Detector . . . . . . . . . . . . . . . . . . . 164

Detector at 77°K . . . . . . . . . . .. . . . . . . . . . . 165

β-Peak Pulse Amplitude from a Germanium Detector . . . . . 166

-vii- UCRL-16231

SEMICONDUCTOR DETECTORS FOR NUCLEAR SPECTROMETRY

Fred S. Goulding

University of CaliforniaLawrence Radiation Laboratory


July 30, 1965

FOREWORD

These lectures were prepared for presentation at the Summer School

for Physicists to be held in Herceg-Novi, Yugoslavia, August, 1965. For

the most part they constitute a collection of essential information on

the detectors and associated systems. Although some important contri-

butions by other groups to the topic are discussed, no effort has been

made to present a detailed review of the voluminous literature on the

subject. Therefore, the notes given here must be regarded largely as

an account of the work of one group in this field. Very few experimental

results obtained with semiconductor detector spectrometers are included

as this material should be covered by other speakers at the meeting.

-1- UCRL-16231

DESCRIPTIVE THEORY OF SEMICONDUCTORSLECTURE 1.

Fred S. Goulding

Lawrence Radiation LaboratoryUniversity of CaliforniaBerkeley, California

July 30, 1965

1.1 INTRODUCTION

Much of nuclear physics research is concerned with the measurement of

the energy of radiation emitted by nuclei undergoing energy transitions.

Consequently, the development of nuclear structure studies has depended

largely upon techniques of accurate energy measurement. The most precise

energy measurements are based on the effect of magnetic fields in bending

the path of electrically charged particles. However, the poor geometrical

efficiency and the inability of such devices to allow simultaneous measure-

nents over a wide range of energies restrict the usefulness of these tech-

niques except for primary standard energy measurements. The high data

accumulation rate of a pulse amplitude analyzer fed by a detector which

totally absorbs photons or particles to produce a signal linearly propor-

tional to the energy absorbed has made these techniques very useful for

general nuclear energy measurements. Gridded ionization chambers and

scintillation detectors have been used in such systems and, in recent years,

semiconductor detectors have assumed increasing importance.

In our laboratory, semiconductor detectors have almost completely

replaced scintillation and gaseous detectors in all nuclear structure work

ranging from work with natural alpha, beta and gamma radiations to nuclear

reaction studies in the 10 to 100 MeV range. The reason for this sudden

change lies primarily in the improvement in energy resolution obtained by

Lecture 1. -2- UCRL-16231

use of these detectors, an improvement which ranges from about 2:1 for low-

energy alpha particles to 10:1 for high-energy (~100 MeV) alpha particlesIand 20:1 for gamma-rays of medium energy (~600 keV). As compared with

gaseous detectors the small size of semiconductor detectors and theirIability to totally absorb the energy of fast electrons and other particles

are additional factors in favour of semiconductor detectors. When compared

with NaI (T1) and other scintillator crystals, the gamma-ray efficiency of

presently available semiconductors is poor, in general, but our experience

is that good energy resolution is more important than very high efficiency

which can usually be compensated for by using more active sources.

While a detailed examination of the problems of energy spread in detector

systems will be made in Lecture #3 it is desirable that we briefly review

here the basic reasons for the improved energy resolution in semiconductor

detectors. In gaseous detector systems electrical noise in the pulse

amplifier and statistical fluctuations of ion-pair production in the detector

both limit the accuracy of energy measurements. For a 5 MeV alpha-particle

(a typical particle in ion chamber applications) about 2 x 105 ion pairs will

be produced assuming that 25 eV are required on the average to produce an ion

pair. If normal statistical variations existed in this number, an RMS fluctu-

ation of about 500 ion pairs might be expected. As pointed out by Fano1,2 RMS

fluctuations will be less than this by a factor of about 0.6.* Therefore, RMS

fluctuation will be about 300 ion pairs. The electrical noise in existing . .high quality amplifiers contributes an effective RMS input signal fluctuation

of about 300 ion pairs also and by adding these two sources of spread in quad-

rature we find that the total effective fluctuation should be about 420 ion

pairs RMS or 1000 ion pairs** full width at half maximum (FWHM is used in the

*The Fano factor (= Mean Square Fluctuation

Av. No. of Ion Pairs

) is assumed here to be 0.4.

**For Gaussian noise the ratio of FWHM/RMS is about 2.3.

Lecture 1. -3- UCRL-16231

remainder of this text). The theoretical FWHM energy resolution for gaseous

ion chambers is therefore about 20 keV. In most practical situations this

result is not realized and 30-40 keV is more common.

Scintillation detectors suffer from quite different sources of signal

spread. The inefficiency involved in the scintillation mechanism, light

collection and photo-emission from the cathode of the photomultiplier, results

in large statistical fluctuations in the number of photo-electrons emitted by

the photo-cathode for a given amount of energy absorbed in the scintillating

crystal.* In the case of a NaI (T1) scintillator-photomultiplier system, at

least 300 eV of energy is absorbed in the crystal for every photo-electron

released. For a 300 keV gamma-ray this results in a FWHM spread of about

25 keV or almost 10%. The energy distribution of electrons produced in the

scintillatar by one gamma-ray may differ considerably from that produced by

another and since the scintillator light output is not a linear function of

electron energy a further spread in light output for gamma-ray interactions

is introduced.4,5 This effect becomes important for high gamma-ray energies,

Fortunately the phototube is a noiseless amplifying device and, apart from

minor contributions due to statistical variations in the numbers of electrons

released by the secondary emission surfaces, it does not further degrade the

output signal.

Detectors employing direct collection of ionization in certain solids

possess one striking fundamental advantage over scintillation and gaseous

detectors. In single crystal semiconductors of the types considered here, a

hole-electron pair is produced for about every 3 electron volts (on the average)

absorbed from the radiation. This figure is almost a factor of 10 smaller than

the equivalent quantity for gaseous detectors and a factor of 100 smaller than

*We will not deal here with the details of the scintillation mechanism.Refer to Ref. 3 for details.

Lecture 1 -4- UCRL-16231

that for scintillation detectors. For this reason, statistical fluctu-

ations in the charge prdouction process in the detector are small. Moreover,

since the charge flow in the detector is almost 10 times larger than in the

gaseous detector, the effect of pulse amplifier noise is reduced by a similar

factor. Unfortunately collection of ionization in solids is, in general, a

difficult process and some rather rigid requirements must be placed upon the

character of the solid. Our next section will discuss these requirements

and the characteristics of suitable material.

1.2 PROPERTIES OF SOLID-STATE DETECTOR MATERIALS

IWe will assume initially that the detector consists of a rectangular

block of material with electrodes in good electrical contact with two opposite

faces of the block. A potential is applied to the electrodes to produce an

electric field in the solid which will (hopefully) sweep out any electrical

carriers produced by an ionizing event. Carriers of both polarities (negative

electrons and positive holes) will be produced in equal numbers by the ionizing

event. As we wish to measure the quantity of ioniaation produced (which is

proportional to the energy absorbed from the radiation) it is important that

the charge flow in the external circuit of the detector be equal to the total

ionization or to some definite fraction of it. In practice the latter possi-

bility is impossible and we are forced to meet the first condition.

The material properties of importance are as follows:

(a) The average energy ε required to produce a hole-electron pair should

be as small as possible. The reasons for this requirement are

apparent from the previous discussion. A portion of ε is used to

lift electrons through the band gap from the conduction to valency


(b)

(c)

band and the remainder is wasted in thermal losses (principally

to optical modes of vibration) in the solid. As a general rule

this factor favors materials with small band-gaps but the situation

is complicated by other factors.

The material should contain few free carriers at the operating

temperature as such carriers will be swept to the electrodes in

the same way as those produced by the ionizing events and will tend

to spread and conceal the wanted signals. This requirement immedi-

ately eliminates conductors from consideration and since, in semi-

conductors and insulators, the thermal activation of electrons

across the band-gap is a mechanism for production of free carriers,

it, favors wide band-gap materials. Since this conflicts with

property (a) a compromise is necessary and the ideal compromise will

depend upon the operating temperature. To be of interest materials

must produce thermal generation currents in the volume of the

detector smaller than 10-7 amperes. For some applications even

smaller currents than this are required.

The previous requirement suggests that an insulator might be ideal

if a rather high value of ε is tolerable. However, it is very

important that the material used should not contain significant

numbers of trapping centers capable of holding electrons or holes

produced by the ionizing events. If this were to happen we would

lose part of our signal with disastrous consequences. This require-

ment immediately narrows down the choice of materials to those

available as almost perfect single crystals (free of impurities to

levels of about 1 part in 109 or better and free of crystal imperfec-

tions). Moreover materials having wide band-gaps tend to contain


many deep trapping centers and are therefore eliminated on this

count. We will characterize the trapping process by the trapping

lifetime of a carrier τT which is the average time a carrier

exists in a free state before being trapped

(d) Recombination of holes and electrons during the charge collection

process must be very small. In practice, recombination occurs

primarily through the intermediary of trapping at energy levels

near the middle of the band-gap. It is of interest to note that

this is related to the property (b) as the primary source of

thermally generated conduction electrons in semiconductors is a

double-jump process whereby an electron in the valency band is

excited info a trapping level near the middle of the band gap and

then re-excited into the conduction band. Recombination in a semi-

conductor is characterized by the carrier lifetime τR and we desire

this to be large compared with the charge collection time.

(e) The effect of both trapping and recombination must be related to

the carrier collection time τC if the magnitude of the carrier loss

is to be evaluated. Ideally the collection time τC should be very

short which demands that both holes and electrons should be highly

mobile in the lattice. Also the material should be able to support

high electric fields without secondary ionization resulting. In

most cases, surface effects limit the applied voltage more than

bulk effects.

(f) The nuclear properties of a material are also important in its

application for detectors. Other things being equal one would

like to use materials containing elements of high atomic number to


improve the absorbtion properties of the detector. These require-

ments are secondary to the electrical requirements discussed in

the previous paragraphs which must be met if satisfactory detection

is to be achieved. However, the nuclear requirements will certainly

influence future work on materials and have already resulted in the

use of germanium for gamma-ray detectors in preference to silicon

which, in most other respects, is a preferable material.

1.3 SEMICONDUCTOR PROPERTIES OF SILICON AND GERMANIUM

Only two materials are known to approach the requirements of the previous

section. Early work in the semiconductor device area (e.g., transistors) was

based largely on using germanium and the extensive program of research and

development on this material resulted in it becoming available in the form

of highly pure single crystals. Later, emphasis on higher temperatures of

operation for semiconductor devices resulted in silicon becoming available

with quality equal or even superior to germanium. These two materials are

now the only ones we are able to use for accurate nuclear spectrometry. We

will now digress from our main topic to consider the properties of silicon

and germanium as examples of a general class of semiconductors.

1.3.1 Intrinsic Material Properties

Both silicon and germanium crystals are particularly simple in their

structure. Fig. 1.1 shows the arrangement of the atoms in a simple valency

bond model of a pure crystal of silicon or germanium. Each atom (valency 4)

is seen to have its valency bonds oriented equally in space and to donate

a single electron to each bond with its four neighbors. Each bond therefore

contains a pair of electrons giving a particularly stable structure.


At very low temperatures all valency electrons are bound into the

structure and no electrons are available to take part in electrical

conduction. Therefore these materials are insulators at these temperatures.

At higher temperatures a small number of the covalent bonds are broken by

thermal excitation so that electron-hole pairs are produced in the material.

In the energy band model, electrons are said to be thermally excited from

the valency to conduction band. The quantities of such electron-hole

pairs clearly depend upon the temperature and the band-gap (binding energy

in the valency bond model). Under normal conditions the number ni of con-

duction electrons in the material (called intrinsic since no impurities

are present) is given by:

where A is a constant for a given material,

T is the absolute temperature (°K),

Eg is the band gap,

k is Boltzman's constant.

At normal temperatures the exponential term dominates the temperature

dependence.

Once an electron is in the conduction band it is influenced by any

electric field applied to the crystal. In normal electric fields this

influence is small compared with effects due to the fields produced by

atoms in the lattice itself but the applied electric field causes a slow

drift of the electrons whereas the effects of the crystal atoms are random


in nature. We can characterize the movement of the electrons in the applied

electric field by a mobility µe defined by the relationship:

(1.2)

where Ve = average electron drift velocity in the field direction

and E is the electric field.

The positively charged hole left in the valency structure is also free

to move* in the electric field. Its movement is characterized by a mobility

µh defined in the same way as that for the electron in equation (1.2).

Combining the currents due to electrons and holes we see that the resistivity

of the material is given by:

ρ =1

q (neµe + nhµh) (1.3)

where ρ is the material resistivity,

nh is the number of holes/cc,

ne is the number of conduction electrons/cc, and

q is the electric charge.

For intrinsic material, every electron excited into the conduction band

produces a hole too so that ne = nh = ni:

... ρ i =

1

q ni (µh + µe) (1.4)

Using the constants listed in Table 1.1 we find that:

ρi for germanium is about 65 ohm/cm, and

ρi for silicon is about 230 x 10-3 ohm/cm,

both values being derived at 300°K. At 77°K virtually no electrons are

*This can be interpreted as a retrograde motion of electrons from filledpositions in the band structure to fill the hole or more correctly, asan alternative quantum mechanical behavicur of the electrons in thevalency band.


excited into the conduction band and intrinsic silicon and germanium are

excellent insulators at that temperature.

The carrier mobility µ, as well as ni, is temperature dependent. The

dependance of µ on temperature in very pure crystals of good quality is

dominated by lattice scattering (i.e., interactions of thermal lattice

vibrations with the electron wave travelling in the structure). As the

temperature is reduced, the mobility increases. For example, µh for

silicon changes from 480 cm2/V. sec at 300°K to about 2 x 104 cm2/V. sec

at 77°K. The temperature dependance of µe, µh and ni is indicated in

Table 1. Fig. 1.2 shows the bahaviour of µe and µh in silicon and

germanium over a wide temperature range.

1.3.2 Extrinsic Material General Properties

In practice, semiconducting materials of sufficient purity to be

regarded as intrinsic, particularly at low temperatures, are not available

to us. Generally speaking, the term intrinsic is used rather loosely to

imply that electrical conduction is dominated by thermally excited electron-

hole pairs rather than by electrons or holes produced by impurities. Thus,

at high enough temperatures we can refer to any semiconductor as being

intrinsic. In the case of germanium it is possible to purify the material

to the degree where the material is intrinsic at room temperature. To

accomplish this, impurities* must be reduced below about 1013 atoms/cc

(i.e., 1 part in 5 x 108) which is just possible. For conduction in silicon

to be considered intrinsic at room temperature, the impurity concentration*

would have to be reduced to about 1010 atoms/cc (i.e., 1 part in 5 x 1011)

which is not practicable. Therefore, for most practical purposes, we have

*We refer here only to electrically active impurities.


to deal with materials in which conduction is dominated by electrical

carriers introduced by impurities in the silicon or germanium. This is

known as extrinsic material and the conduction is termed extrinsic too.

The electrically active impurities most commonly deliberately intro-

duced into semiconductors are elements of valency 3 or 5 which can sub-

stitute for silicon atoms at lattice sites. Thinking in terms of the

valency bond model we can regard a valency 5 atom (e.g., phosphorous,

arsenic, antimony) which replaces a silicon atom in the lattice as

supplying the electrons to complete the co-valent bond structure while

the fifth electron associated with the impurity atom is only very loosely

bound to its parent atom by Coulomb attraction. This attraction is very

small partly due to the fact that the atom is embedded in a medium of high

dielectric constant (12 for silicon, 16 for germanium). At normal tempera-

tures the spare electron is thermally excited into the conduction band so

that we now have a free electron and a fixed localized positive charge

embedded in the lattice in the vicinity of the impurity atom. Such impur-

ities are called donors and, since the electrical conduction in such

materials is dominated by negative charge carriers, the material is said

to be n-type. Conversely, replacement of silicon atoms by valency 3 atoms

(e. g., boron, aluminum, gallium, and indium) produces holes and fixed

negative charge centers; the material is p-type and the impurity is called

an acceptor. In an energy band model the effect of donors is to introduce

permitted discrete levels (localized in the vicinity of the impurity atoms)

in the forbidden gap close to the conduction band. Conversely the effect

of acceptors is to introduce levels close to the valency band. Donors and

acceptors such as these are easily ionized. Table 1.2 lists the ionization

energy for some of these cases.


In detector technology we are particularly concerned with a number of

other types of center in the lattice. For the present we will note that

an interstitial atom can act as a donor or acceptor giving free holes

and/or electrons. A good example of this is lithium which acts as a shallow*

interstitial donor in silicon and germanium. Certain other impurities

acting in a substitutional or interstitial role like gold in silicon or

copper and nickel in germanium introduce acceptor and/or donor levels near

the middle of the forbidden gap. Note that certain impurities can introduce

both donor and acceptor levels. We can picture this as depending upon the

position occupied by the impurity atom in the lattice. For example, gold

introduces both an acceptor and donor level near the middle of the energy

gap. As one might expect, a valency 2 substitutional impurity tends to

produce a double acceptor while a valency 6 substitutional impurity tends

to produce a double donor.

Another matter of concern to us is the number of traps in the material.

These traps may arise due to impurity centers or crystal imperfections

(vacancies, dislocations, etc.) and may exhibit preferential trapping pro-

perties for either holes or electrons. The traps are of interest in that

they provide intermediate levels in the forbidden gap through which recom-

bination and generation processes can take place. Moreover, if the traps

are selective for holes (or electrons) and the trapped carriers are not

easily re-excited, localized storage of electrical charge may occur and

this may inhibit collection of carriers in the device. This is particularly

important in low temperature operation of devices and is the cause of the

phenomena generally referred to as polarization in detectors.

*The term shallow implies that the level introduced by the impurity isclose to the conduction band (donor) or valency band (acceptor).


1.3.3 More Detailed Behaviour of Carriers in Extrinsic Material.

Considering, for the moment, intrinsic material in equilibrium, an

average number ni electrons occupy the conduction band and a similar

number of holes exist in the valency band. We have to remember that this

equilibrium results from the balance between excitation of electrons into

the conduction band (called generation) and by electrons falling back into

holes in the valency band (recombination). The rates of generation and

recombination can be increased by introducing traps into the forbidden

gap as these traps provide the potential for a double step process which

can clearly proceed at a faster rate than if electrons have to jump across

the whole energy gap in one step. Traps at the center of the energy gap

are most effective in increasing the generation and recombination rate as

the two steps are then equal. Despite the increased rate of recombination

and generation the equilibrium density of electrons and holes is the same

in material containing large or small numbers of such traps. In a non-

equilibrium condition, however, in which an applied electric field sweeps

out carriers immediately they are produced, the high generation rate induced

by traps considerably increases the leakage current and, from this point of

view, traps (particularly in mid-band) are undesirable. We will pursue

this point later.

Now let us examine the introduction of a small amount of a donor impurity

into the semiconductor. This increases the number of electrons from ni to n.

Let the consequent alteration in the hole population be from ni to p. The

recombination rate between hole and electrons must be proportional to the

product (n · p) of the numbers of such carriers present in the material. We

can assume that the generation rate is only dependent upon valency bonds

which are far more numerous than the impurity atoms. Since the thermal

generation rate (at impurity levels commonly encountered) is therefore the

same as for intrinsic material and the recombination rate in such material

is proportional to ni2 we can write:

2n · p = ni (1.5)

Thus we see that the effect of increasing the electron population by

adding donors is to suppress the hole population to satisfy equation (7.5).

Similarly, if we introduce acceptors, the electron population is reduced.

These remarks apply at a fixed temperature; if the temperature is changed,

ni must be chosen for the new temperature.

To appreciate the effect of this minority carrier suppression by

introducing majority carriers we may examine the case of silicon at room

temperature 300°K). In this case, ni = 1.5 x 1010/cc. Let us now

introduce 1.5 x 1011 donors/cc (i.e., about one atom in 4 x 1010). The

hole population will now only be 1.5 x 109 - a factor of 100 smaller than

the electron population. Conduction in such a sample is now dominated

by electrons and the resistivity is given by:

ρ = 1 (1.6)

neµe q

In our example, ρ would be 35000 ohm/cm. In practice removal of impurities

to this extent is impractical. However, the float-zone process in silicon

can produce material in the 10000 ohm/cm (p-type) region. Figs. 1.3 and

1.4 show the resistivity as a function of donor and acceptor concentra-

tion for silicon and germanium.

We must now examine the behaviour of these extrinsic semiconductors

as the temperature is changed. At high temperatures (~150°C for very pure

silicon and ~60°C for very pure germanium) the value of ni increases so

Lecture 1 -15-

that, in the doping range of interest to us (~ 1012 to 1016 impurity

atoms/cc) electrical conduction hecomes dominated by thermally excited

carriers and the material is called intrinsic. As the temperature is

lowered, conduction is dominated by the majority carriers and the quantity

of these remains essentially the same down to temperatures at which the

donor or acceptor centers become unionized (i.e., ~ 10 to 50°K). In

lightly doped material the mobility is determined by lattice scattering

and the mobility-temperature relationships shown in Table 1.1 apply.

However, as the lattice scattering becomes smaller the effect of the

Coulomb attraction of impurity atoms becomes more important and mobility

becomes determined by impurity scattering. Even at moderate doping

levels this effect causes the mobility to level off or decrease below

about 200°K. Fig. 1.5 shows the mobility temperature relationship for

some samples. In closing these remarks on mobility we must point out

that, since the number of carriers remains essentially constant in extrinsic

semiconductors over a wide range of temperatures while the mobility increases

as the temperature decreases in the range where lattice scattering is

dominant, the result is that the material exhibits a high positive

temperature coefficient of resistance as seen in Fig. 1.6 over part of

the temperature range. This is a surprising result on the basis of

traditional views of semiconductors.

In the preceeding discussion we assumed that the extrinsic semiconductor

was produced by adding either an acceptor or donor to intrinsic material.

Usually, however, we are dealing with materials containing both donor and

acceptor atoms. Since we have seeen that the addition of donors to a

material produces the hole population so that equation (1.5) is satisfied,

it is obvious that addition of donors compensates for acceptors.


If Na = number of acceptors and Nd = number of donors and Na = Nd the

material behaves very much like intrinsic material. However, the impurity

scattering effect mentioned earlier in this section will still occur and

the mobility-temperature relationship will not behave as it would for

intrinsic material. The departure would be especially noticeable if Na

and Nd were large. An exception might occur if the donor was lithium.

In this case, the positively charged lithium atoms may be mobile enough

to migrate close to the acceptor atoms and to pair (i.e., be tied by

Coulomb attraction) with the negatively charged acceptors. At distances

of a few lattice constants the electrical effect of the electrical dipole

containing the two atcns might well be negligible and the effects of

impurity scattering on carriers is much reduced.

One final concept which must be discussed is that of minority carrier

lifetime. For this purpose, we will assume that we are dealing with p-type

material in which electrons are the minority carriers. We will suddenly

introduce a number ne electrons into the conduction band. Clearly these

electrons must eventually disappear by recombining with holes in the valency

band. The number of electrons remaining at time t will be given by:

nt = ne e-t/τR (1.7)

where τR is the recombination lifetime.

The probability of the electron making the direct jump to recombine with a

hole in the valency band proves to be very small (lifetimes of many seconds

would occur in silicon if this were the only mechanism whereas the very

best silicon exhibits lifetimes in the 1 to 10 msec range). As mentioned

earlier, the presence of traps at or near the center of the band gap speeds

up recombination. The statistics of the electron capture and emission process

I


at traps and the same processes for holes has been studied by Shockley6

and we do not need to consider the details here. However, one can

intuitively see that the lifetime will be reduced in the presence of

large numbers of traps and that the availability of large numbers of holes*

(i.e., heavily doped p-type material) also reduces the lifetime. In

practice, high temperature treatments tend to produce lattice irregular-

ities which act as traps and reduce lifetime. The presence of gold in

very minute quantities in silicon introduces trapping levels with high

cross-section in the center of the band gap and thereby reduces carrier

lifetime by many orders of magnitude. In view of these factors it is

surprising that carrier lifetimes in the range 20 to 2000 µsec are normal

in fully processed detector materials.

1.4 JUNCTIONS IN SEMICONDUCTORS

1.4.1 Descriptive Junction Theory

We have so far discussed only homogeneous semiconductor materials.

While the properties of such materials are interesting, practically all

applications of semiconductors to detectors and other devices rely on

discontinuities between regions of a semiconductor having different

properties. The most important discontinuity is that existing between

two regions, in cne of which the host lattice is doped with a donor

(n-type) while the other is doped with a acceptor (p-type). We must

examine a p-n junction of this type in some detail if the operation of

semiconductor devices and particularly detectors is to be understood.

This argument must be reversed if we are talking of the lifetime of holesin n-type material. Here the hole lifetime is reduced in heavily dopedn-type material.


In Figure 1.7(A) the case of a junction with the n side more heavily

doped than the p side is illustrated. The acceptor and donor centers are

fixed in the lattice and cannot move. However the free holes and electrons.

can move and, at temperatures above absolute zero, diffusion of these

carriers across the junction takes place. This, in turn, results in the

, .

dipole charge layer shown in Fig. 1.7(B) which produces the potential

distribution shown in Fig. 1.7(C). The potential hill at the junction is

such as to resist the carrier diffusion process and, therefore, its height

depends upon the temperature, doping levels, etc. The p-type material

contains some free electrons and, in the n-type material, some holes are

produced by thermal excitation of electrons from the valency to conduction

bands of the silicon host lattice. Since, in our case, the doping of the

n-type material is much heavier than that of the p-type material, the

density of minority electrons in the p-region will be large compared with

that of minority holes in the n-region. In equilibrium a detailed balance

must exist both for holes crossing the junction and for electrons. This

means that the hole currents to left and right must equal each other and

the electron currents each way must also equal each other. In our case

the absolute value of the electron current will be very much larger than

that of the hole current as illustrated in Fig, 1.7(D). The individual

hole or electron currents in a junction can well be in the range of many

amperes.

The equilibrium conditions are greatly disturbed if: we apply an

external voltage to the junction. For example; applying a negative voltage

to the n side of the junction (called forward bias) causes a large increase

in the flow of electrons from the n side of the junction (where they are


majority carriers) into the p side where they are minority carriers. This

process is called minority carrier injection. At the same time an increase

in the number of holes injected from the p to n sides occurs. As the doping

on the p side is very light the hole current will be negligible compared

with the electron current. The phenomena of minority carrier injection

is of major importance at the emitter junction of a bipolar transistor.

1.4.2 Reverse Biased Junction

In detector technology we are more concerned with reverse biased

operation of junctions. Examining Fig. 1.8 we see what happens in this

situation in our example of a junction with a lightly doped p-region. Free

carriers are swept from a depletion layer of thickness W by the electric

field and the dipole layer consists almost entirely of fixed donor and

acceptor atoms (fully ionized). Since the charge density in the lattice

is constant in each region (but different between the regions) it is

easy to see that the electric field must be linear as a function of dis-

tance either side of the true junction. This results in the parabolic

potential distribution shown here. In a case where the n-region doping

is very heavy almost the entire junction voltage drop appears in the p-

region as seen in Fig. 1.3. In this simplified case, which applies to

almost all radiation detector situations, the width W is given by:

1/2

W =κ (V + Vo)2π q Na

(1.8)

where κ is the dielectric constant of the material.

Na is the net density of electrically active centers in the

lightly doped region (if the material is compensated Na is

the difference between acceptor and donor concentrations).

Vo is the junction built-in potential in the equilibrium situation

(~ 0.7 V for Si, 0.3 V for Ge).


The value of the maximum electric field Ep in a junction of this

type is given by:

Ep = 2(V + Vo)

W (1.9)

This value may be of interest for two reasons. If Ep reaches values

greater than 2 x 104 V/cm secondary ionization may arise. Although this

would not be expected on the basis of theoretical values for the avalanche

breakdown field (~ 250 kV/cm) experience has shown that most junctions,

particularly of the large area type used in detectors, are not completely

uniform. This results in peak fields far exceeding the value calculated

from equation (1.9). A second factor also arises at high field strengths.

If the carrier velocity (= E · µ) reaches a value close to the velocities

of thermal agitation of electrons in the lattice (~ 107 cm/sec) the

carrier velocity tends to become independent of the electric field. This

may be important in collection time calculations. The limiting velocity

for electrons in germanium has been studied16 but information on holes in

germanium and holes and electrons in silicon indicates that the saturation

effect is not so apparent in these cases.

1.4.3 Junction Capacitance

When an ionizing particle passes into the depletion layer of a reverse

biased junction a specific amount of charge is collected by the electric

field. The voltage pulse developed across the junction is inversely

proportional to the sum of the junction capacitance and the input capaci-

tance at the input of the pre-amplifier used to amplify the signal. It

is obvious that the signal-to-noise ratio of the system is determined by

the input signal voltage and is therefore degraded if the detector capacity

is large. For this reason we need to determine the junction capacitance.

Lecture 1 -21-

The depletion layer of a reverse biased junction behaves much like

an insulator with metal electrodes at either side of it. If the thickness

of the depletion layer is W cm and its area A cm2, its capacitance is

given by:

(1.10)CD = 1.1-4πWκA pf

where κ is the dielectric constant of the material.

For silicon:

CD 1.1 AS -WpF (1.11)

For germanium:

CD 1.37= A-W pF

1.4.4 Junction Leakage Currents

(1.12)

Leakage currents in reverse biased p-n junctions arise from three

sources. In the junction of Fig. 1.8 the three sources are:

(a) Minority holes from the n region which diffuse from a region

near to the edge of the depletion layer into the depletion layer.

If a hole enters the depletion layer, the electric field causes

it to move rapidly across into the p-region.

(b) Minority electrons in the p-region which diffuse from a small

layer at the right hand edge of the depletion layer. Once in

the depletion layer the electrons travel rapidly into the n-type

material. The mathematical treatment of the hole "diffusion"

current and that for electrons is the same. It will be clear

that the relatively heavy doping of our n-region means that the

: hole population in it is very small and that the electron

current from the p-region will dominate as far as these diffusion

currents are concerned. We will therefore only analyze its

behaviour. The symbols used are shown in Fig. 1.8.


The electron current arises from thermal excitation of

carriers within a diffusion length Le of the edge of the depletion

layer. The volume of material involved in generating the electron

diffusion current is therefore A·Le. In equilibrium this volume

would contain A·Le·np electrons and since each of these would exist,

for an average time τe the recombination current would beA·Le·np·q

τeIn the case we are now concerned with, these electrons flow

into the infinite sink which the depletion layer forms for electrons

We therefore have:

Diffusion current iD = A·q·np·-τee (1.13)

(Note that we assume that the average occupancy of the recombination

centers by holes is not significantly affected by the removal of

the small number of electrons which would be present in the

equilibrium situation.)

Other forms of equation (1.13) can be derived using Einstein’s

relationship. The most useful is:

(1.14)

Where ρp is the resistivity of the p-type material.

If the constants for silicon at room temperature are inserted

in this equation we obtain:

16 ρpiD(Si-25°C) = nA/cm

2

τe1/2

where ρp is expressed in K Ω · cm.

and τe is µsec.

- (1.15)


In a typical case for a diffused silicon junction detector

ρp = 1 K Ω · cm and τe = 50 µsec. Here we see that iD is

2.3 nA/cm2 of junction area.

(c) In junctions operated with very thin depletion layers (e.g.,

signal diodes, transistors) the diffusion current will constitute

the main bulk leakage current. However, for obvious reasons,

thick depletion layers are necessary for radiation detectors.

Here the generation current of electrons and holes in the large

volume of the depletion layer may well become dominant as the

electric field existing in this layer causes the carriers to

be collected before they have the opportunity to recombine.

Unfortunately, knowledge of the position of traps in the band-

gap is required if an accurate calculation of this generation

current is to be made and knowledge of the lifetime of carriers

in the material in equilibrium is not adequate for the purpose.*

If the traps are assumed to be at the center of the energy gap

and with certain other simplifying assumptions the value of the

generation current, i.g., in the depletion layer is:

ig = A·W·q·ni2τ - (1.16)

In general this equation will overestimate the leakage current

by a factor between 2 and 20 depending on the position of the

traps in the band-gap.

(1.17)

We can rewrite equation (1.16):

κ· ρp·µh (V + Vo)1/2 ig = A· -·

ni2τ2π

*In the case of calculating the difffusion current we assumed that the smallloss of electrons did not affect the average occupancy of the traps. Ina depletion layer, however, holes are removed immediately they are formedand the trap occupancy is quite different from that applying in theundepleted material.

I


When the constants for silicon at room temperature are included

in this equation we obtain:

.ig = 1.2 (ρV)1/2

τeµA/cm2 (1.18)

where ρ = p-type material resistivity in K Ω · cm.

τe = electron lifetime in the p material in µsec.

If ρ = 1 K Ω cm and τe = 50 µsec and V = 100 V

ig = 0.25 µA/cm2 of junction area.

Note that this is two orders of magnitude higher than

the diffusion current calculated earlier.

1.4.5 P-I-N Junctions

Examining Equation (1.9) we note that the depletion layer may be

made very thick by reducing Na (i.e., increasing the resistivity of the

p-region in our example) and by increasing the applied voltage V. If

the thickness of the slice is suitable, it is possible to "punch through"

the wafer or make the depletion layer reach the back of the wafer. If

a simple metal contact or an n region vere used as the back contact,

electrons would be injected by the contact and be swept up in the field.

This would cause a very high junction current. Indeed, even if the

depletion layer did not quite reach the back contact injection from the

contact would still be serious. For this reason, where the detector is

designed for punch-through operation a highly doped (designated p+) region

is deliberately introduced as the back contact (if the basic material is

p-type). Such a device is referred to as p-i-n (incorrectly implying an

intrinsic region between p and n regions) or p-π-n, or more correctly,

a n+p p+ punch-through device (the + sign meaning highly doped). Such a

device and its electric field, potential and charge distribution is shown


diagramatically in Fig. 1.9. Most of the voltage drop in the device

occurs in the p-region and the electric field can be made high through

the entire p-region - which is nearly the entire thickness of the

wafer. If the p-region is very lightly doped and the electric field is

below a value at which carrier velocity saturation occurs, the collection

time for a carrier making the complete transit across the depletion

layer is given by:

TC = W2-µ·V (1.19)

For example, if W = 0.1 cm, µ = 500 cm2/V sec (a hole in silicon) and

V = 200 Volts then TC = 0.1 µsec.

The thermal generation current of a p-i-n diode can be calculated

from equation (1.16) with the assumption that traps are at the middle

of the energy gap. If the carrier lifetime in our example were 1 msec

the generation current would be 0.16 µA/cm2.

1.4.6 Metal to Semiconductor Surface Barrier Junctions

All the forementioned types of junctions are encountered in radia-

tion detectors. An additional one for which no very satisfactory theory

exists is used in many radiation detectors. This is the so-called

surface-barrier junction. Certain metals such as gold, when evaporated

onto an n-type silicon or germanium surface form a rectifying barrier

which behaves in many ways like a true p-n junction. The preparation

of the surface prior to and following evaporation involves certain

emperical procedures which are believed to form en oxide layer. However,

this is not the only factor as studies have shown some relation between


the work function of the evaporated metal and the behaviour of the

surface barrier. While the simple processes involved in making surface

barrier devices are attractive the lack of basic understanding of

the mechanism leads to serious problems. We will not devote any

further discussion to this type of device.


Table 1.1. Some Properties of Silicon and Germanium+

SILICON GERMANIUM UNITS

I

Atomic Number Z 14 32 -

Atomic Weight A 28.06 72.60 -

Density (3OO°K) 2.33 5.33 g/cc

Dielectric Constant κ 12 16 -

Melting Point 1420 936 °C

Band Gap (300°K) 1.12 0.67 eV

Band Gap (T°K) 1.205-2.8 x 10-4T 0.782-3.4 x 10-4T eV

Intrinsic CarrierDensity (300°K) 1.5 x 1010 2.0 x 1013 per cc

Intrinsic CarrierDensity (T°K) 2.8 x 1016T3/2e-6450/T 9.7 x 1015T3/2e-4350/T per cc

Electron Mobilityµe (300°K) 1350 3900 cm

2/volt sec.

Hole Mobilityµh (300°K) 480 1900 cm

2/volt sec.

Electron Mobility(T°K) 2.1 x 109T-2.5

* 4.9 x 107T-1.66

* cm2/volt sec.

Hole Mobility(T°K) 2.3 x 109T-2.7

* 1.05 x 109T-2.33

* cm2/volt sec.

Energy per HoleElectron Pair 3.75** 2.94 eV

+ Data largely obtained from E. M. Conwell, Proc. IRE 46, 1281 (1958).

* Measured only over a limited temperature range (about 100-300°K for Germanium)and 160-400°K for Silicon).

** Recent measurements in our laboratory. Measurements by some authors indicatea difference between the value of ε in silicon for electrons and α particles,(α-3.61, ε-3.79) but we are inclined to attribute this to a charge multipli-cation phenomena at the surface barrier employed by these authors.


Table 1.2. Impurities in Ge & Si

ELEMENT TYPE

IONIZATION ENERGY (eV)

In Silicon In Germanium

Boron Acceptor 0.045 0.0104

Aluminium " 0.057 0.0102

Gallium " 0.065 0.0108

Indium " 0.16 0.0112

Phosphorus Donor 0.044 0.0120

Arsenic " 0.049 0.0127

Antimony " 0.039 0.0096

Lithium " 0.033 0.0093(Interstitial)

-29-

LECTURE 1. FIGURE CAPTIONS

UCRL-16231

Fig. 1.1 Unit Cell of Single Crystal Si and Ge.

Fig. 1.2 Variation of Mobility with Temperature in Pure Samples.

Fig. 1.3 Resistivity - Impurity Concentration for Si.

Fig. 1.4 Resistivity - Impurity Concentration for Ge.

Fig. 1.5 Effect of Impurities on Mobility.

Fig. 1.6 Resistivity Temperature Relation for an Extrinsic Silicon Sample.

Fig. 1.7 Diagram of a P-N Junction in Equilibrium.

Fig. 1.8 A Reverse Biased P-N Junction.

Fig. 1.9 An N+PP+ Punch-Through Diode.


FIG I.IUNIT CELL OF CRYSTAL OF Si & Ge

a

NO. OF BONDS/ UNIT CELL = 16

NO. OF ATOMS/ UNIT CELL = 6

VALUE OF aSi - 5.43 Å

Ge - 5.66 Å

NO. OF ATOMS/cc

Si - 6.22 x 1021

Ge - 5.53 x 1021

MUB-6960

-39- UCRL-16231

LECTURE 2. SEMICONDUCTOR DETECTOR TECHNOLOGY AND MANUFACTUREFred S. Goulding

Lawrence Radiation LaboratoryUniversity of California


July 30, 1965

2.1 INTRODUCTION

Two major differences exist between the problems involved in making

semiconductor elements such as transistors and diodes and those encountered

in making nuclear radiation detectors. In radiation detectors we are

usually dealing with device areas in the region of a few cm2 while modern

transistors have areas in the region of 10-4 cm2. Also, since the parti-

cles we detect and measure may have substantial ranges in the material, the

thickness of our sensitive region must be in the range of .01 to 1 cm

whereas the equivalent region in transistors and signal diodes is only a

few microns thick. Thus, our sensitive volume is ~108 times more than

that normally encountered in semiconductor technology. It is perhaps

surprising that so many of the techniques used in the transistor field

have been almost directly applicable to the field of radiation detectors.

However, it should not surprise us that limitations not encountered in

transistor production do arise in detector technology. The basic semi-

conductor electronics outlined in the previous paper applies to either

situation but, apart from the use of similar techniques such as diffusion

processes, the contents of this paper are of major interest mainly in the

detector field.


2.2 DISCUSSION OF PURITY OF SEMICONDUCTOR MATERIALS

As we saw in the previous paper the production of thick sensitive

regions in semiconductor detectors depends upon the availability of very

high resistivity silicon and germanium. The material used in semiconductor

detectors is made by a zone-levelling process whereby a floating zone is

passed through a crystal several times. Most of the impurities in the

silicon or germanium prefer to remain in the liquid phase so that the

re-crystallized material behind the zone contains a reduced impurity

concentration as compared with that in front of it. By successive passes

of the zone along the rod, impurities are concentrated at one end and can

be removed by cutting off the end. A limitation exists in this process due

to the diffusion of impurities from the crucible material which holds the

silicon or germanium. Commercially produced germanium is purified by a

zone refining process in a quartz crucible and adequate reduction of

impurity concentrations for normal semiconductor devices is achieved. This

implies that impurity concentrations of less than 5 parts in 108 can be

achieved since this corresponds to the carrier concentration in intrinsic

germanium at room temperature. However, if such germanium is cooled to

77°K, its carrier concentration will remain close to the value it had at

room temperature which is much too high for thick detectors. Similarly

with silicon, the impurity concentration which can be produced by zone

levelling in a crucible is not adequate to give silicon of sufficiently

high resistivity for detector use. A zone-levelling process in which a

self-supporting liquid zone is passed through a rod of silicon is used to

produce the very high purity silicon now used in radiation detectors. This

is known as the floating-zone method and no crucible is required for it.


It is usually carried out in vacuum, heat being supplied by R.F. induced

eddy-currents and the walls of the tube surrounding the vacuum are water

cooled to reduce contamination.

Unfortunately, with all precautions discussed in the previous para-

graph, silicon which is intrinsic at room temperature and germanium which

is intrinsic at 77°K are not available from zone-refining processes. In

silicon, one limitation arises due to the fact that boron exhibits a very

small segregation coefficient between the liquid and crystal phases. For

this reason most high quality silicon is p-type. Difficulties are also

experienced with removing the last traces of oxygen in silicon and germanium.

While oxygen is not electrically active in its normal state in silicon and

germanium it can produce electrically active centers when the material is

processed at high temperatures and can affect the material properties

adversely.

For these reasons there are severe restrictions on the sensitive

thickness of detectors made with commercially available silicon and germa-

nium. In fact, germanium in its commercially available form is now never

used in detectors. A substantial part of the effort in detector manufactur-

ing processes therefore consists of deliberately compensating the unwanted

impurities in silicon and germanium to produce very high resistivity (or

nearly intrinsic) material. We will examine the compensation processes

later but will now deal with the case of silicon detectors made with no

compensation process.

2.3 DIFFUSED SILICON DETECTORS

2.3.1 Elementary Considerations

The p-n junction described in 1.4 provides one method of using zone

refined silicon for radiation detection and measurement. In the commonest


form of such a detector a thin n-type surface layer is produced on one

face of a high resistivity p-type bulk. The best method of producing the

n-type layer is by solid-state diffusion of a donor element (usually

phosphorus) from a phosphorus-containing vapor into a silicon wafer which

is held at a temperature in the range 800 to 1200°C. While this process

is similar to that used in all modern semiconductor devices, the diffusion

depth must be made very small in p-n junction radiation detectors as the

ionizing particles usually enter the bulk through the surface diffused

layer. For this reason diffusion schedules are short and temperatures

are low compared with those used in conventional semiconductor technology.

The doping level of the surface n-layer produced by this process will be

very high and the sheet resistance will, in general, be less than 10 ohm/sq.

To use a p-n junction as a radiation detector, reverse bias is applied

to the junction to produce a depletion layer as described in section 1.4.2

The thickness of the depletion layer obeys equation (1.8) and this relation-

ship is shown graphically in Fig. 2.1. Fig. 2.1 also shows the relationship

for the case of a heavily doped p-type surface layer on n-type bulk. The

depletion layer is expressed in terms of the room temperature resistivity

of the bulk silicon and the applied voltage. As silicon of the necessary

quality is only relatively readily available in the resistivity range of

100 ohm cm to 10000 ohm cm, depletion layer thicknesses of p-n junction detec-

tors operated at 300 V (which is a typical value for good detectors) are

in the range 50 to 500 microns for p-type material or 100 to 1000 microns

for n-type material. Material toward the top of the resistivity ranges is

difficult to obtain and tends to be highly compensated. High temperature

heat treatments usually change such materials considerably. For these


reasons a good practical limit to assume for the thickness of diffused

detectors is .05 cm (i.e., 500 microns). This limits their use to

measurement of fission fragments, p-particles up to about 500 keV,

natural alpha particles and the lower energy range of machine-produced

particles.

Due to the relatively small thickness of the depletion layer the

capacity of the junction tends to be quite large, which, as we shall see

in Lecture 3, places a limitation on the energy resolution which can be

obtained. Using a detector of 1 cm2 area having a depletion layer thickness

of 200 microns (detector capacity = 55 pF), electrical noise limits energy

resolution to about 7 keV FWHM (using present day preamplifiers). To this

figure we must add any signal spread due to other factors such as the

statistics of hole-electron pair production in the detector.

So far we have discussed only the elementary principles of a diffused

junction detector. Unfortunately the simple model used would not be a

good device and several years of development effort have been required to

overcome its deficiencies. Before describing a process for making high

quality diffused detectors, two major sources of difficulty must be

discussed. Surface effects at the junction edge justify a separate section

of the paper. However, we will start by dealing with the question of charge

injection by the back contact of the device. In Fig. 2.2(A) the simple

structure of a n-p junction detector is shown. An ionizing particle enter-

ing the depletion layer leaves behind a track of ionization and the electric

field due to the applied voltage causes the holes and electrons to separate.

The electrons move up to the n+ contact and disappear into the highly doped

region. The holes drift down into the undepleted p-region. Therefore, a

localized positive charge is introduced into the p-region. This produces a


slight local positive potential to occur in the region where the pulse of

holes enters the undepleted p-material. This situation clearly cannot

exist for long,* and, in general, is corrected by a movement of holes in

the p-material away from the region and into the evaporated metal contact

(process (1) in Fig. 2.2 (B)). However, it is quite possible for a

localized n-region to exist at the metal contact as shown in Fig. 2.2(B).

In this case a second mechanism (2) exists to correct the potential rise

in the p-material. An electron may now be injected into the p-material

from the n-region. This electron will then exist as a minority carrier in

the p-material and will diffuse in the material until it either recombines

with a hole, or until it reaches the boundary of the depletion layer, in

which case it will rapidly travel across the depletion layer (3) in Fig. 2.2(B).

If this happens, charge over and above the original ionization will flow in

the internal circuit and a multiplication effect occurs.

The consequences of this are shown in Fig. 2.2(C). In a detector

which does not exhibit this effect, the Am241 alpha-particle spectrum

has the general form shown as (a). However, a detector exhibiting the charge

multiplication phenomena gives a pulse amplitude spectrum as in (b). In

severe cases multiple peaks have been observed.

In order to ensure that multiplication of this type does not take place,

it is now common to diffuse a p+ layer on the back surface. We normally use

boron as the diffusant and the diffusion depth is made about 2 µ. This en-

sures that no n-regions exist on the back surface and that the mechanism (2)

in Fig. 2.2(B) is eliminated. The virtual absence of electrons in the p+

layer means that electrons are not available for mechanism (2).

εThe dielectric relaxation time for the material is equal to 1.1 -

4 π x 10-12

sec. For 1000 ohm cm silicon this is 1.1 nsec.


2.3.2 Surface Properties

It would be no exaggeration to say that the least understood and

most time-consuming aspect of semiconductor devices is the behavior of

the region where a junction intersects the surface of the crystal. The

objective of all the work on this problem can be stated simply as being

to establish desirable initial surface conditions and to minimize changes

in the surface properties during the useful life of the device.

Fig. 2.3 shows two typical surface conditions which can be produced

by chemical treatments or ambient effects at the surface of a p-type

wafer the front face of which contains a diffused n+ region. In the

first case, the surface behaves as a lightly doped n-type layer and

forms a "skirt" (or "channel") on the diffused n+ region. When reverse

voltage is applied to the main junction, the junction between the n-type

channel (close to the n+ region) and the p-type bulk is also reverse

biased and a depletion layer forms in this region as well as in the n+

region. The n-type surface channel is, in general, only lightly doped

and the leakage current from it into the bulk must flow through the

channel. In consequence a voltage gradient exists along its length and

the channel-bulk junction is only reverse biased to a limited distance

from the edge of the n+ region - this distance usually being referred to

as the channel length. On high resistivity p-type silicon it can extend

for substantial distances - we have measured channel lengths of up to

0.5 cm in reverse-biased diffused junctions. The junction between the

n-type surface channel and the bulk is a particularly poor one and pro-

duces substantial leakage currents which, in most simple junction diodes,

far exceed the bulk generation and diffusion currents discussed in section

1.4.4. As we saw in 1.4.4(B) the diffusion current across a reverse


biased junction arises from minority carriers generated within a diffusion

length of either side of the junction. The surface layer contains a high

density of traps in the forbidden band-gap and the thermal carrier generation

rate is very high. Therefore the lightly doped n-type surface layer acts

as a copious source of holes which are injected across the depletion layer.

If the layer is made more n-type, the channel extends further and the

surface generated current flow in the external increases.

The opposite situation is represented in Fig. 2.3(B). Here we have a

p-type surface and the depletion layer does not extend along the surface.

However, at the junction between the p-type surface and the n+ region, only

a very thin depletion layer exists. As the reverse bias is increased, the

high electric field across this peripheral junction causes avalanche break-

down and high leakage currents. As the surface is not generally uniform

the breakdown is not sharp as in avalanche diodes but causes a fairly rapid

rise in current as the reverse bias is increased beyond a certain value.

The contrast between the two cases is obvious in the measured character-

istics of junction detectors. An n-type surface is characterized by high

leakage but no breakdown at high voltages while a p-type surface shows low

leakage at low voltages but a rapid increase of leakage above a certain

voltage. Curves obtained by T. M. Buck7 are shown in Fig. 2.4 as an illus-

tration of this behavior. In this case, changes in the ambient atmosphere

are seen to produce large changes in the leakage characteristics. A gross

difference also exists in the characte r of the electrical noise produced by

the leakage current in the two cases. In the case of the n-type surface

the noise behaves much as simple current noise with a reasonably flat

frequency distribution but, in the p-type case, the noise contains a larger

proportion of low frequency noise and tends to be very "spiky" as seen on


an oscilloscope. For these reasons, the ideal surface is lightly n-type

and chemical treatments are aimed toward achieving this ideal.

A method of making the diode characteristics less surface dependant

is to use the guard-ring structure described by the present author and

W. L. Hansen8 in 1960. Fig. 2.5 shows the structure. Here, a narrow

isolation ring is etched through the n-type diffused surface layer thereby

dividing it into two regions. The central region is used as the detector

and signals are taken from it. The outside region - called the guard ring -

is connected to the same bias potential as the central region but its

leakage current does not flow in the load resistor and produces no signal.

As far as the central region is concerned, its surface channel can only

extend out across the etched isolation ring and the surface area of the

channel is very small. Thus, by treating the surface to make it lightly

n-type, the central region leakage current can be made very small. Fig. 2.6

shows a typical characteristic for the central region. The guard-ring

leakage, on the other hand, is similar to that of a normal diode due to

the surface channel surrounding it. The impedance between the central and

outside regions is very low for small detector bias voltages due to the

n-type surface channel across the etched isolation ring. However, increasing

the detector bias causes the surface channel to deplete and the inter-

electrode impedance becomes very large ( ~ 1000 M ohm) so that it does

not significantly shunt the load resistor R2:

Unfortunately, as can be observed in the ambient effects shown in

Fig. 2.4, an unprotected surface at the edge of a p-n junction is subject

to the effects of the prevailing atmosphere and, consequently, such a

detector changes its properties over a period of time. Attempts to protect


the surface with various "painted-on" products such as epoxies, silicones,

glasses melting at low temperatures, etc., have, in general, proved

unsatisfactory partly due to their own adverse electrical effects and

partly due to their failure to provide complete long-term protection.

For some time, it has been recognized that a thermally grown SiO2 protective

layer offers the best possibilities for surface passivation. This process

was first used in making transistors and has been responsible for one or

more orders of magnitude improvement in the reliability of semiconductor

devices. It is illustrated in Fig. 2.7 which shows the steps used in

preparing a junction using a planar technique. Two key features deserve

comment:

(a) The phosphorus does not diffuse through the oxide coated surfaces.

(b) The edge of the junction is produced under the oxide and, if the

oxide is not removed after this time, the junction edge is never

exposed to ambient gases.

Efforts to accomplish oxide passivation of silicon junction detectors have

involved a lengthy development program due to the formation of an n-type

(inversion on p-type material) layer at the Si-SiO2 interface. This inver-

sion layer causes a very long surface channel resulting in very large

detector leakage.

We have now successfully accomplished an oxide pascivation process and

the details of it will be discussed in section 2.3.3. However, before

dealing with the process in some detail, we will briefly discuss certain

aspects of the behaviour of the Si-SiO2 interface. The n-type layer

observed at the Si-SiO2 interface in early experiments suggested the possi-

bility of compensating the donors by diffusing an acceptor impurity into


the silicon prior to oxide growth. This was successfully accomplished

using gallium as the acceptor impurity9 (gallium was chosen due to its

low surface concentration during diffusion end also because oxide

growth tends to deplete it from the bulk) but the temperature-time

diffusion parameters were very critical and difficulties were encountered

in obtaining good yields from the process. Further investigation of the

mechanism involved in the formation of the n-type layer indicated that the

"strength" of the layer was not a function of the oxide-growth itself but,

instead, was entirely controlled by the ambient atmosphere present in the

furnace tube during the phosphorus diffusion and in the cooling period

following the diffusion.10 The presence of oxygen causes strong inversion

layers due, probably, to formation of SiO4 complexes in the Si surface

layers. Formation of these complexes is inhibited by the presence of

hydrogen. The presence of nitrogen produces many traps at the interface

and these, by reducing the carrier mobility in the surface layer tend to

reduce the length of the surface channel. Control of these parameters

allows the production of excellent diodes without the use of gallium

surface compensation.

2.3.3 Preparation of Diffused Detectors.

The process described in this section is one used to produce quantities

of detectors in our Laboratory. Different processes exist in other labor-

atories but the steps described here will serve as a guide to anyone inter-

ested in developing his own process.

(i) Wafers are cut on a diamond saw from p-type floating-zone silicon.

The resistivity is usually in the range 100 ohm cm to 10000 ohm cm,

and typical wafer thicknesses are from 40 to 80 x 10-3

cm.


(ii) The wafers are lapped with 10 micron Al2O3 lapping compound, either

on a lapping machine or by hand on a Pyrex plate. About 13 x 10-3 cm

is removed from each side in this operation.

(iii) The wafer is etched all over in a standard 3:1 HNO3-HF etch for

1-1/4 to 1-1/2 minutes. This removes about 5 x 10-3 cm from

each side thereby taking off the regions damaged by lapping.

(iv) Oxide is removed from the surface of the wafer by immersion in HF

for 1 to 2 minutes. The HF is rinsed off with CH3OH and then with

C2HCl3 (trichlorethylene).

(v) After this cleaning step, the wafer is immediately put into a

tube furnace where the boron diffusion is carried out. The

diffusant is BI3 vapor with a reducing carrier gas* which conists

1000°C. The flow of BI3 vapor is then stopped and diffusion is

continued for a further 2 hours in the reducing atmosphere. This

schedule produces a boron diffused layer of 2.7 microns thickness.

The sheet resistance is in the range 4 - 8 ohm/sq. The furnace

is allowed to cool below 700° before removing the wafer.

(vi) One side of the wafer (which will be referred to as the back from

now onwards) is painted with a material capable of resisting the

etch. We use Picein 80.** The remainder of the wafer is then etched

in the 3:1 etch for 45 seconds which completely removes the boron

from the unprotected side.

(vii) The Picein is washed off in C2HCl3 and the wafer is cleaned as in

step (iv). A further cleaning step consists of leaving the wafer

in H2O2 for a brief period and washing again with CH3OH and C2HCl3.

of about 90% nitrogen mixed with about 10% hydrogen. The boron

predeposit under these conditions is carried out for 1 hour at

*Gas flow rates in all cases are 1/2 l/min.**Made by New York Hamburger Gummi-Waaren Compagnie, Hamburg 33


(viii) The wafer is immediately inserted into the tube furnace where

oxidation takes place. Oxidation is in a steam atmosphere

generated in a quarts boiler and is carried out at 1000°C for

2 hours. The oxide thickness resulting from this is about

0.7 microns. The tube is flushed out with nitrogen for a few

minutes prior to allowing steam to enter it and nitrogen is also

introduced when the steam is turned off. (Nitrogen flushes through

all furnaces at all times to prevent the entry of air into the

furnace tubes.) The furnace is cooled to less than 700°C before

the wafer is removed.

(ix) The wafer is coated with Picein on the back and the required

geometry is painted on the front using Picein (in the case of a

simple diode the geometry consists of an uncoated central disc

while the region outside it is coated; a guard ring device has a

more complex geometry) the oxide in the unprotected regions is

now dissolved off by immersing the wafer in ammonium bi-floride

for 3-4 minutes.

(x) The silicon surface is then etched in 20:1 HNO3, HF for 1 minute.

This removes about 1 micron of silicon.

(xi) Picein is washed off with C2HCl3 and the wafer is thoroughly

cleaned as in steps (iv) and (vii).

(xii) The wafer is immediately put into the furnace tube where the phos-

phorus diffusion takes place. The initial predeposit is made for

40 seconds in an atmosphere of POCl3 in O2. Nitrogen then flows

through the furnace tube for 3 minutes and this is changed to a

reducing gas (90% N2 10% H) for 7 minutes. This is then changed


back to nitrogen for a further 20 minutes. The whole of this

process is carried out at 900°C and the furnace is allowed to

cool to almost exactly 600° before removing the wafer.* A

modification is made to the above process when using materials

of resistivity less than 400 ohm cm. In this case the hydrogen

step is omitted to achieve the right final surface condition.

(xiii) The front of the wafer is coated with Picein and the oxide is

removed from the back by immersing the wafer in HF for 1 minute.

(xiv) The Picein is removed in C2HCl3 and the wafer is thoroughly

cleaned and dried. It is then dipped for 6-8 seconds in a very

weak oxide etchant** to remove a very thin layer off the surface

of the oxide.

(xv) We now have a complete detector and evaporation of gold contacts

on the n+ and p+ areas completes the operations.

The performance obtained from detectors made by this process will be

illustrated in a later part of this paper. We will now return to the

topic of making detectors having sensitive regions much thicker than those

attainable in diffused detectors.

*If the furnace is allowed to cool below about 500°C or lower before removingthe wafer, a drastic change in the electrical character of the Si-SiO2 inter-face takes place.

**The weak etch used for removing a thin layer from the surface of the oxideconsists of 60 c.c. of HF mixed into a solution containing 1 lb. ofammonium fluroide in 2 litres of deionized water.


2.4 COMPENSATION BY LITHIUM DRIFTING

2.4.1 General Principles

It is a fortunate circumstance that the behavior of lithium in

silicon and germanium lends itself to producing well compensated almost

intrinsic regions of substantial thickness. The two important properties

which make this possible are the very high mobility of lithium ions in the

valency 4 crystals combined with the fact that the lithium atom acts as a

singly charged interstitial donor atom with a low ionization energy (.033 eV

in Si, .0093 eV in Ge). Other elements have a high mobility in silicon

and/or germanium (e.g., Cu in Ge, Au in Si) and exhibit donor or acceptor

properties but do not behave in a simple calculable fashion like lithium.

Originally this aspect of lithium drifting suggested its use as a tool in

the investigation of the interactions between impurities and defects in

silicon and germanium and the classical work of Reiss, Fuller and Morin11

and, later, Pell was concerned with the use of lithium in such investigations.

The concept of producing thick compensated regions was first conceived by

Pell12 and has found its greatest application in semiconductor detectors.

Since lithium is a donor, all lithium compensation is done in p-type

material. The lithium is usually evaporated onto the surface of the p-type

material,* the temperature is raised to about 400°C and lithium diffuses

into the silicon. After this step, the lithium distribution in the silicon

has the form shown in Fig. 2.8(A) which is represented by the relationship:

ND = No erfc ( x )

2%

where ND = donor concentration at depth x from the surface,

No = lithium surface concentration (~1018 atoms/cc),

to = duration of diffusion,

Do = diffusion constant at the diffusion temperature.

*A suspension of lithium in oil is sometimes used for this purpose.

(2.1)


If the acceptor concentration in the p-type material is NA the p-n junction

will be at a depth xo given by:

NA = No erfc ( xo ) 2%

(2.2)

The value of xo for a 400°C diffusion of 3 minutes duration is about

7 x 10-3 cm for silicon (floating zone). For germanium (almost oxygen free)

a typical diffusion depth is 50 x 10-3 cm after a 5 minute diffusion at

about 450°C.

If reverse bias is now applied to the p-n junction, the lithium ions,

which carry a positive charge, begin to move from the n side of the junction

to the p side where they tend to compensate the acceptor atoms in the p-region.

At quite moderate temperatures the flow of lithium ions across the junction

is large enough to provide enough donors to compensate a substantial volume

of p-type material in a short time. Fig. 2.8(B) shows the situation after

a short period of drifting. It is seen that lithium has moved out of the

n-region to produce an intrinsic region of width W. That the compensation

mechanism will be quite accurate is illustrated in Fig. 2.8(C). Here we

have imagined a pile-up of donors to occur in a region toward the middle of

the intrinsic region. The electric field distribution, shown in Fig. 2.8(D),

indicates that a higher electric field exists to the right of the pile-up

region than to the left. Therefore the current of lithium ions to the right

out of the pile-up region exceeds the current of ions into it from the left.

The piled-up donors therefore very rapidly dissipate leaving an accurately

compensated region.

It is interesting to calculate the rate of growth of the intrinsic region.

For this purpose we will assume that the electric field is high enough for the

current of lithium ions to be almost entirely due to the electric field and


for the diffusion current to be negligible. We will also assume that the

initial period of drift is completed and the situation illustrated in

Fig. 2.8(B) exists. Throughout the intrinsic region NA = ND and the

electric field is V-W where V is the applied voltage. We then have:

Current of Li ions/sq. cm = JL = V -W · µL · NA (2.3)

where µL is the mobility of the lithium ions in the semiconductor

at the drift temperature.

The number of acceptors which can be compensated in time dt is there-

fore JL · dt and, since the acceptor concentration in the uncompensated

material is NA, the increase ∆W in the thickness W of the intrinsic layer

in time dt is given by:

NA dW = V -W · µL · NA dt

... by integration; W2 = 2 V · µL · t

w=J2LLL · V · t (2.4)

For practical purposes this relationship suffices for nearly all

detector drift calculations. It breaks down only at short times when W is

of the same order as the thickness of the lithium diffused n-region. Fig. 2.9

shows this relationship for silicon (V = 500 V) and Fig. 2.10 gives similar

information on germanium (V = 600 V). We note, from equation (2.4) that the

drift rate is independent of the resistivity of the starting material and

that the drift rate can be increased by raising the temperature (since the

Li ion mobility increases as temperature rises) or by increasing the applied

voltage. The value of the latter is usually dictated by diode surface break-

down problems and voltages in the range 500 to 1000 volts are generally

employed. The temperature is subject to an absolute upper limit above which

the material becomes intrinsic and the junction ceases to behave as a diode.


Lower resistivity materials allow higher temperature operation but such

materials, in general, produce poorer quality devices. Moreover, a drift

temperature well below the intrinsic temperature is desirable due to the

fact that a considerable bulk leakage current flows in the device at

higher temperatures. Sufficient lithium resides in any part of the drifted

region to produce electrical neutrality in that region at the drift temper-

ature. As the holes and electrons produced thermally in the drifted

region, during their transit across the depletion layer, constitute charge

in the bulk the lithium concentration adjusts itself to a value determined

by this charge as well as the acceptor charge. This results in the lithium

distribution not being correct to compensate the acceptors. Drifting at a

lower temperature for at least the final part of the drift operation (this

is called levelling) reduces the overcompensation to a negligible amount.*

Typically our silicon detectors are drifted at 130°C and 500 V (see

Fig. 2.9) which means that a 3 mm detector requires about 60 hours to drift.

Germanium detectors are usually drifted at about 40°C and 600 V. An 8 mm

thick germanium detector therefore requires 300 hours to drift.

We see that the drift times involved are quite long and some thought

has been given to reducing these times. One interesting method which has

not yet been employed is to largely compensate a piece of p-type material

by diffusion of lithium in a tube furnace (a closed box system would be

required to prevent the reaction between the lithium and the quartz tube).

We might aim to introduce a fraction F of the lithium required to achieve

complete compensation by this method. The material is then used for a

normal lithium drift process. Examining equation (2.3) we see that the

*This effect can easily be estimated; it is about 1 part in 103 for driftinga 3 mm thick silicon detector made with 1 K ohm cm material drifted at500 V and 1 mA leakage (~125°C).


current of lithium ions across the compensated region is unaltered for

the same width W, but the region dW now contains only (1-F)NA · dW acceptors

which require compensating. Equation (2.4) then becomes:

2 µL · V · tW =(1-F)

(2.5)

If F = 0.9, the value of W achieved in a given drift time would be

about 3 times larger than in silicon (or germanium) not treated by the

partial compensation by diffusion method prior to drifting.

2.4.2 Secondary Effects in Lithium Drifting

A number of secondary effects which occur in the lithium-silicon and

lithium-germanium systems can have very significant effects in lithium

drifting operations and, as these complicate the process, we must deal with

these here in a general way. The effects which lead to complications all

arise from reactions between the lithium and defects in the material such

as vacancies and other impurities. The most important ones are:

(a) Oxygen Content of the Semiconductor.

In both silicon and germanium concentrations of oxygen in

the crystal in the range of 1 part in 109 have a serious effect

in reducing the drift rate of lithium. This is caused by a

reaction between the lithium ions and oxygen atoms forming LiO+

which is less mobile than the Li+ ion. It has been suggested that

this effect might be useful in preventing the movement of lithium

in detectors for use at higher temperatures but its effect in

slowing down the drift process is more important in detector

technology. In order to drift successfully it is necessary to

obtain silicon and germanium almost completely free of oxygen.

Silicon produced by the vacuum floating zone process is suitable


(b)

material. In the case of germanium satisfactory results have

been achieved with material made by carrying out the zone

levelling process in a reducing atmosphere.

Fairing Reactions between Lithium and Acceptors.

The drifting process results only in compensation of any

charge existing in a volume of the material of the order of the

Debye length. No direct association between the acceptor atoms

(e.g., boron) and the lithium ions is necessary for this. However,

as the positively charged lithium ions diffuse they will tend to

be attracted by Coulomb forces to the negatively charged acceptor

atoms. A close association between acceptor and lithium atoms

may therefore result. At high temperatures this "pairing" effect

will be negligible due to thermal agitation processes, but at low

temperatures, if sufficient time is allowed to elapse, the pairing

will be complete and each atom of lithium will be closely tied to

an acceptor atom.

The effects of pairing may be important in detectors from

two points of view. In the first place the binding of lithium

atoms to the acceptor centers can inhibit the movement of these

atoms and thereby stabilize the characteristics of the device. A

second possible advantage accrues from the reduction in impurity

scattering due to the pairing process. As pointed out in 1.3.3,

this has the effect of increasing the carrier mobility at low

temperatures.

Close pairing of a lithium and acceptor atom results in negligible electricfield due to these atoms at a distance and, therefore, little effect oncarriers passing through the material.


Precipitation of Lithium at Vacancies.

In order to compensate for a concentration Na of acceptors,

Na atoms of lithium per cm3 must be introduced into the material.

If Na is larger than the maximum solubility of lithium at room

temperature (or the detector temperature) the material is super-

saturated with lithium and precipitation of the excess lithium

will occur if the lithium atoms can find suitable precipitation

sites. Vacancies in the material provide such precipitation

sites, and when the lithium atoms precipitate they lose their

electrical activity.

This situation is particularly important in germanium. The

initial diffusion process gives a lithium surface concentration

of the order of 1018 atoms/cm3 while the equilibrium solubility

of lithium in intrinsic germanium at 25°C is 6.6 x 1013 atoms/cm3.

Particularly in the material used in early detectors (probably

due to oxygen and surface damage) difficulty was experienced due

to the lithium precipitating in the surface n-region to leave a

p-type surface. A further difficulty can, in principle, arise in

the bulk compensated region. Studies have shown that the equili-

brium solubility of lithium in germanium is smaller than the value

required to compensate material of less than 30 ohm/cm. Therefore,

one must anticipate possible precipitation problems when using

starting material of lower than 30 ohm · cm resistivity.

For lithium precipitation to occur, precipitation sites must

exist and the quantity of these is greatly dependant upon the

quality of the material. It is possible, under certain circumstances,


to fill the precipitation sites with atoms of another element and

thereby to inhibit precipitation of lithium at a later-time. We

once used copper for this purpose13 but, as material quality has

improved, this has ceased to be necessary.

Lithium precipitation does not appear to be a significant

problem in floating zone silicon.

2.4.3 Surface Effects in Lithium Drifted Devices

Unfortunately the planar oxide passivation technique described in

section 2.3.2 has not yet proved to be applicable to either lithium drifted

germanium or silicon detectors.* The failure to develop oxide passivation

is due to the fact that high temperature processing required in oxide growth

introduces impurities and defects in the material which give large generation

(leakage) currents in thick lithium drift detectors. We must therefore resort

to chemical treatments for adjustment of surface states and to paint-on

varnishes for surface protection. Typical treatments are described in the

following sections in which the steps in our production processes for lithium-

drifted silicon and germanium detectors are detailed.

2.4.4 Preparation of Lithium Drifted Silicon Detectors**

(i) Wafers are cut to the required thickness from floating zone p-type

silicon in the resistivity range 500-5000 ohm cm.+ Wafer thicknesses

range from 0.5 to 5 mm.

One commercial manufacturer produces oxide passivated lithium driftedsilicon detectors but the oxide is not thermally grown.

**This process is the one used in our laboratory and might be termed a lowtemperature process as contrasted with methods which use much higher temper-atures. It is to be regarded as illustrative of a general method; variantsare used in other laboratories.

+We find that leakage currents are lower and device performance better at lowtemperatures if material in the top half of this resistivity range is used.One might attribute this to the general poorer quality of the low resistivitymaterial.


(ii) Wafers are lapped with 10 micron AL2O3 lapping compound removing

about 10 x 10-3 cm from both sides. They are thoroughly cleaned

in detergent, methyl alcohol and triclorethylene.

(iii) Wafers are placed on a heater plate in a vacuum evaporator and

heated to 350°C. Lithium is then evaporated from a lithium metal

source onto one side for 30 sec. We continue to hold the wafer

at 350°C for a further 1-1/2 minutes. The hot plate is then

cooled rapidly by passing water through a cooling coil. This

process gives a very uniform lithium diffused region 7.5 x 10-3 cm

thick.

(iv) Wafers are removed from the evaporator and washed with CH3OH to

remove free lithium on the surface. They are then given an

overall 1/2 minute etch in 3:1 HNO3 - HF etchant. This removes

any traces of lithium which may have strayed onto the wrong side

of the wafer.

(v) In preparation for drifting on the automatic drifting apparatus, a

pattern is evaporated (gold) on the back of the wafer (i.e., the

face opposite to the lithium side). The purpose of this pattern,

which consists of a central disc of 3 mm diameter surrounded by

a 1 mm space then by a completely gold-covered outer region,

is to allow the drift apparatus to monitor the approach of the

drifted region to the back.

The central region of the lithium face is masked with Picein to

give a junction of the required area and the whole of the back is

masked too. A 6 minute etch in 3:1 etchant removes all the lithium

diffused region etch depth about 15 x 10-3 cm) except the central

masked area. The etch is quenched in running distilled water and


the Picein is then washed off with C2HCl3 and the wafer thoroughly

cleaned with CH3OH and C2HCl3. The two sides of the wafer are now

as illustrated in Fig. 2.11; on the back is the gold evaporated

structure while the front has the lithium diffused region in a

mesa form.

(vii) The wafer is now put into the drift apparatus where drifting takes

place at about 130°C with an applied voltage of 500 V. A detailed

description of this apparatus has been given by the author and

W. L. Hansen.4 For the purpose of this outline we may say that

the principal feature of interest in the drift apparatus is that

(viii)

ix) The whole front of the wafer and a ring around the periphery of the

it controls the wafer temperature to maintain the device leakage

current during drift at a preselected value in the range 0.5 to

5 mA and constantly monitors the approach of the drifted region

to the back of the wafer. For completely automatic operation the

drift can be terminated by the apparatus when the drifted region

reaches a pre-determined distance from the back. In practice we

allow nearly all our devices to reach the back and over-drift for

a short time.

When drifting is complete, the back of the wafer is lapped to a

depth of about 10-3 cm and a staining procedure* is used to reveal

the location and size of the intrinsic region's intersection with

the back. If the size is adequate (usually about equal to the

mesa area on the front) and the region is uniform, the drifting is

considered to be satisfactory. Occasionally it is necessary to

lap a short distance from the back to satisfy the test.

back is masked with Picein and the remainder of the back is etched

*Immersion in a CuSO4 solution containing a small amount of HF. A brightlight is necessary to obtain a good stain.


for 3 min in 3:1 etchant and quenched in running distilled water.

This produces a well in the back about 7.5 x 10-3 cm deep. The

Picein is now removed with C2HCl3 and the wafer is washed with

CH3OH and C2HCl3. A final clean up overall etch of 1/2 minute

in 3:1 etchant water is then given to the wafer and the etch is

quenched with running distilled water.

(x) The wafer is now thoroughly cleaned by scrubbing with a cotton

swab immersed first in C2HCl3 then in CH3OH and washed in CH3OH

and C2HCl3. It is then soaked in HF for about 1 minute, washed

briefly with CH3OH and dried in a jet of dry nitrogen. It is

then left in room air in a covered dish for about 16 hours.

(xi) Gold is now evaporated over the entire back of the wafer and

also onto the contact region on the lithium diffused front.*

(xii) The wafer is now ready for final setting of surface states. To

carry this out we first scrub the periphery of the mesa with a

cotton swab dipped in CH3OH then wash briefly with CH3OH. The

front of the wafer is then covered with HF for 30 seconds. This

removes all oxide on the surface and leaves a very n-type surface.

Washing with CH3OH for about 15 seconds produces a neutral or

lightly n-type surface. In all cases we measure the characteristics

of the diode at this stage and rewash with CH3OH until the desired

surface is achieved.**

*The gold back to the intrinsic region produced by this process is usuallyregarded as a surface barrier. However, in our case we believe that thegold only contacts a shallow p-region produced by the etching process atthe surface. This belief is supported by the fact that scratching the golddoes not affect performance and also by the observation that use of a slowetch in step (vii) produces a thick dead layer at the surface.

**As was seen in 2.3.2 an n-type surface is characterized by fairly highleakage hut no breakdown at high voltages and a p-type surface by the opposite situation.


(xiii) The periphery of the mesa is now coated with a polyurethane

varnish which is allowed to dry for about 24 hours before the

device is used. The polyurethane provides good protection and

has negligible effect on the surface properties established

in step (xii).

2.4.5 Preparation of Lithium-drifted Germanium Detectors

NOTE: Partly due to the size and mass of the pieces of material used

(often ~ 6 cm3) and also due to the brittle nature of germanium, the

handling of this material is much more difficult than that of silicon. For

this reason all heating and cooling operations are made slowly to avoid

thermal shock. Also sawing operations are made in several steps -- we slice

0.5 cm at each pass.

(i) Horizontal single crystal zone-levelled material obtained from

Sylvania is employed. This is supplied in the form of an ingot

of up to about 12 inches length with a cross section which is not

rectangular but is about 4 cm wide at the bottom, 3 cm at the top

and 2-1/2 cm high.

(ii) Cut the detector blocks from the ingot on a diamond saw. (Here,

for example, the material and the pitch used to cement it onto

the ceramic mount are heated quite slowly to avoid thermal shock.)

We usually cut the blocks a little over 1 cm thick except for

special thin detectors.

(iii) Lap the faces of the block with 10 µ Al2O3 lapping compound. This

is done manually with light pressure using a pyrex lapping plate.

(iv) The Ge block is placed on a moveable stainless steel plate in a

vacuum evaporator. A heater near the stainless steel plate is

heated to 450°C. The vacuum is pumped down and lithium is evaporated


down onto the face of the germanium block. The stainless steel

plate holding the germanium block is then moved over onto the

heater and dry nitrogen is admitted to the vacuum belljar to give

heat conduction between the heater and the steel plate. Under

these circumstances the germanium requires about 2 minutes to

reach 450°C. It is left on the heater for another 5 minutes

(this gives about a 0.5 mm thick diffused region). The stainless

steel plate with the germanium block on it is then moved onto a

water cooled plate; in 2 minutes the germanium is cooled and can

be removed from the belljar.

(v) The excess lithium is washed off in distilled water. The sides

of the germanium block are now cut off on the diamond saw to

give a rectangular germanium block 2 cm x 3 cm x 1 cm (typical).

(vi) The edges of the block are lapped and washed and the whole german-

ium block is etched for 1-1/2 minutes in standard 3:1 HNO3:HF with

6% (by volume) of red fuming nitric acid added to the etch to speed

up the start of the etching process.

(vii) Side surfaces are now treated chemically to reduce leakage currents

which will flow in the device during the drift step which follows.

The best treatment we have found consists of a 1 minute etch in

3:1 HNO3:HF plus red fuming HNO3 as in (vi); quench with CH3OH;

30 seconds in 30% aqueous NH3; a brief quench in CH3OH; 20 seconds

in 30% H2O2. During these-treatments the front and back faces of

the device are protected by an etch-resistant adhesive tape.

(viii) The tape is removed and the device is inserted in the drifting

unit. In this unit, illustrated in Fig. 2.13, the detector is

clamped between a pair of thermo-electric coolers with an indium-

Lecture 2 UCRL-16231

gallium eutectic alloy between the faces of the detector and

cooling plates. The coolers are insulated electrically from

the actual cooling plates holding the device so that reverse bias

can be applied to the detector via these plates. Power to the

coolers is controlled by a circuit in such a way that the thermo-

elements either heat or cool the detector to maintain its leakage

current at a preselected value. The drift voltage is approximately

500 volts and the current through the detector is selected to give

a temperature in the range 30-60°C. Initially, this means that the

preset demand-current might be 10 mA and the thermo-elements are

operating mainly in a heating mode to maintain the leakage at the

10 mA value. The detector temperature might be 60°C. Later, as

the drifted region becomes thicker and the thermal generation

current increases, the preset demand-current will be increased to

~ 60 mA to keep the temperature up to about 35°C and the thermo-

elements will now be operationg mainly in the cooling mode to pump

out the 30 watts of heat being generated by the leakage in the

detector.

(ix) When calculations indicate that drifting has reached the desired

depth (usually 8 mm), the device is removed from the drifter and

the drifted region is revealed by a staining technique. This

consists of immersing the device in a solution of about 20 g/litre

of CuSo4 in water at 25°C with a reverse bias applied to the

junction such that up to 50 mA flows in the detector. This

immediately reveals the periphery of the depleted region.


(x) If the desired drift depth has been achieved the device is given

a 30 sec etch all over. The front and back faces are now taped

with etch resistant tape and the 1 minute etch and chemical

surface treatment described in (vi) is repeated.

(xi) The tapes are removed and the detector is mounted in its holder.

The thermal contact is improved by using a thin indium foil

between the detector and the cold plate with a thin smear of

indium-gallium eutectic between the detector and the indium foil.

The eutectic is also used between the opposite face of the detector

and its contact point to give good electrical contact. We often

find it necessary to thoroughly clean the holder with organic

solvents and dry it thoroughly immediately before mounting the

detector. A diagram of the type of holder and cryostat used at

Berkeley is shown in Fig. 2.14. After mounting the detector the

vacuum is pumped down to 10-5 mm of Hg, and the system is then

cooled down to liquid nitrogen temperature. After a few minutes

the vacuum ion-pump is switched on and the unit can be used. The

preamplifier mounts directly on the side of the holder with a

connection to the detector which has very low shunt capacity

to ground.

2.5 DETECTORS NOT EMPLOYING JUNCTIONS

In our first discussion of semiconductor detectors we assumed that the

device might consist of a block of semiconductor with metallic contacts at

either side. The reader may wonder why we became involved in p-n junctions

and departed from the simple concept. In fact the earliest semiconductor

detectors used diamonds and the simple metallic contact approach was employed.


Later gold-doped silicon, which behaves much like intrinsic silicon at

liquid nitrogen temperature, was used. Both these approaches have now

been displaced by the p-n junction devices we have discussed.

A major reason for this is that metallic contacts, if they behave in

an ohmic fashion (i.e., not rectifying) allow free passage of holes or

electrons from semiconductor to metal and vice versa. Thus if an ionizing

event produces a hole-electron track in a detector of this type made of

very lightly doped n-type material, the electrons may be quickly swept out

of the material by the electric field while the holes move more slowly.*

Thus while the holes are being collected a localized positive charge exists

in the material. To compensate this positive charge, electrons will be

injected from the more negative contact of the device. These electrons

travel rapidly across the material and still more electrons are required

to correct the charge unbalance. Thus a rather unpredictable charge multi-

plication effect occurs and a large spread in signal amplitude may result,

If the more negative contact were a p+ contact almost no electrons could

be injected into the material in the manner described. This is the basic

reason for using the p-n junction device.

We have used a grossly oversimplified model in this explanation. In

fact, the existence of a localized positive charge will only cause injection

of electrons after a time of the order of the dielectric relaxation time of

the material, (i.e., 1.1ρ · K4 π x 10-12 sec) and, if the collection time

is short compared with this, no multiplication will occur. One must

attribute the success of the early detectors to this. On the other hand,

it is difficult to make ohmic contacts to high resistivity material and it

is possible that the devices behaved as surface barrier detectors. The

*If traps which selectively trap one carrier are present in the material,the effect described here is enhanced.

I

I


behaviour of the p-n junction is more predictable and this is the reason

for its general superiority for nuclear spectrometry.

2.6 MAKING THE CHOICE BETWEEN DETECTOR TYPES

In planning an experiment which might use semiconductor detectors the

choice between the various types of detector might not be obvious to the

physicist since the lithium-drifted silicon detector's areas of applications

overlap those of both lithium-drifted germanium and diffused silicon. We

will therefore attempt here to indicate the specific advantages and limitations

of each type.

Oxide-passivated diffused detectors possess the paramount advantage of

long-term reliability due to the complete surface protection offered by the

oxide. They can be made in a totally depleted form and, in this case, the

dead layers at front and back are very thin ( ~ 0.5 µ). This is an important

feature if a detector is to be used as a DE detector in a particle identifier

system. Conversely, if the detector is not totally depleted, the thickness

of the sensitive region can be varied by changing the applied voltage. This

can be useful in discriminating between long-range and short-range particles.

A further advantage of the diffused detector as compared with the other types

is its relative insensitivity to radiation damage. This results from the

high acceptor or donor concentration in a diffused detector compared

with lithium drifted detectors. Against these advantages must be set the

limited thickness of the sensitive region which reduces the range of

particles which can be stopped and also gives a high detector (electrical)

capacity with consequent relatively poor resolution due to electronic noise.

Diffused detectors are used primarily for natural and low-energy

machine-produced particles (resolution a 15 keV FWHM on natural alphas),


β-particles (resolution a 8 keV FWHM at 300 keV), fission fragments and

heavy ions. The majority of our diffused detectors are used for fission

fragments and heavy ions as radiation damage is a serious problem in this

work. Good diffused detectors made of 400 ohm cm silicon can withstand up

to 108 - 109 fission fragments for sq. cm. before becoming unusable. In

nearly all these applications the detectors are used at room temperature

although recent tests have indicated good operation and improved radiation

life when irradiated with fission fragments at liquid nitrogen temperature.

Lithium-drifted silicon detectors find the widest range of uses. The

ability to make fairly thick sensitive regions which give low capacity and

allow the detector to totally absorb particles of a wide range of energies

contribute to their versatility. Cyclotron produced particles (for example

alphas in the energy range 10 to 120 MeV) are commonly measured with these

detectors. In this case, the detectors are generally used at room temper-

ature as the electrical noise due to the detector leakage current produces

a small signal spread compared with other sources. On the other hand, by

cooling the detectors,* high resolution β-particle spectroscopy becomes

possible. Resolution (FWHM) figures of 3 to 5 keV are obtained. These

detectors also find application in low energy gamma-ray spectroscopy

(up to 50 keV) where the thin dead layers on both faces of the wafer absorb

fewer gamma-rays than do the much thicker dead layers on germanium detectors.

Cooled lithium-drifted silicon detectors may also be used for natural alpha-

particle spectroscopy but the dead layers on these detectors are not as well

controlled as those on diffused detectors and this can be a source of trouble.

Some silicon detectors show polarization effects due to deep lying trapsat liquid N2 temperature. We usually cool silicon detectors at -50°C to -100°C.


Lithium-drifted germanium detectors must always be used at low temper-

atures (77°K is convenient and is generally used) in order to reduce the

leakage current and its noise. However, the higher atomic number of german-

ium compared vith silicon, the ease of drifting very thick (1 cm) devices,

and the lower energy required per hole electron pair all favour germanium

as compared with silicon for most gamma-ray spectroscopy. At low energies

the dead layers* at either side of the sensitive region absorb a large

fraction of the gamma-rays -- a factor which favours silicon at the present

time.

In conclusion we might say that the choice of detector is usually

fairly obvious and, in cases where it is not, the choice is usually a

compromise between a number of factors which can only be evaluated in terms

of the specific experiment.

*In general the dead layers have been at least 25 x 10-3 cm thick. Recentlywe have demonstrated that a gold back can be made to the intrinsic regionyielding a very thin access window. It remains to be seen whether thisprocess can be reproduced. Tavendale15 has reported results for a thinwindow germanium detector made by drifting right up to an aluminum alloyed

Fig. 2.1

Fig. 2.2

Fig. 2.3

Fig. 2.4

Fig. 2.5

Fig. 2.6

Fig. 2.7

Fig. 2.8

Fig. 2.9

Fig. 2.10

Fig. 2.11

Fig. 2.12

Fig. 2.13

Fig. 2.14

-72- UCRL-16231


Depletion Layer Thickness Curves for N end P-Type Silicon.

Illustration of Charge Injection at Rear Contact.

Models of Surface Layers at Junction Edge.

Effect of Ambients on Leakage Current of a Junction (T.M. Buck).

Guard-Ring Structure.

Typical Leakage Curve for Guard-Ring Detector.

Steps in Preparing a Planar Junction Device.

Distribution of Lithium at States of Lithium Drift.

Drifted Region Thickness - Time Relationship for Silicon.

Drifted Region Thickness - Time Relationship for Germanium.

Illustration of Silicon Wafer Prior to Drifting.

Cutaway View of Lithium-Drifted Silicon Detector.

Germanium-Lithium-Drift Unit.

Diagram of Germanium Detector Holder and Cryostat.

UCRL-16231

LECTURE 3. FACTORS DETERMINING THE ENERGY RESOLUTION IN

MEASUREMENTS WITH SEMICONDUCTOR DETECTORS

Fred S. Goulding


July 30, 1965

3.1 INTRODUCTION

It is difficult to give a general account of the problems of achieving

high-resolution in semiconductor detector measurements as several inter-

related factors are involved in the final result. In some applications one

set of factors is dominant while an entirely different set may be of crucial

importance in another case. Some of the factors are under the control of

the experimenter (such as counting rate, optimazation of amplifier time

constants, etc.), others are of a semi-fundamental nature (such as vacuum

tube noise) while yet others are truly fundamental in nature (e.g., statistics

of charge production in the detector). In each experiment it is necessary to

appreciate which factors are important and to optimize the parameters accord-

ingly. In this paper we will deal in some detail with the fundamental and

semi-fundamental limitations and in less detail with other factors which may

be encountered. Finally, an effort will be made to indicate types of experi-

ments in which different factors are likely to be important.

In discussing the energy resolution capability of detector systems we

must choose a standard of comparison between them. The standard is always

based upon the equivalent spread in signals at the input to the system but

the particular one employed by a writer often depends whether he is primarily

concerned with designing electronic systems or is concerned with the physical

aspects experiments. In the former case, the signal spread is usually quoted


in terms of the equivalent number of ion pairs corresponding to the signal

spread at the input to the amplifier. To translate this into energy absorb-

tion in the detector, the physicist allows for the value of the average

energy required to produce an ion pair in his particular detector. Most of

the results on preamplifier noise are expressed here in terms of the

equivalent RMS input quoted in ion (or hole-electron) pairs. On the other

hand, the experimental results will be expressed as the full width at half-

maximum of a peak in an energy spectrum (EFWHM). For peaks with a Gaussian

shape this corresponds to about 2.3 times the RMS energy spread. If two or

more sources of uncorelated spread are present their effects must be added

2in quadrature (i.e., ETOTAL =Z+T+1 "2 ......).

3.2 STATISTICAL SPREAD IN THE DETECTOR SIGNAL

If all the energy lost by ionizing particles (or gamma-rays) in a detector

were converted into ionization, signals produced by monochromatic radiation

quanta or particles would show no fluctuations.* On the other hand, if the

energy was mainly dissipated in thermal heating of the lattice and the pro-

bability of an ionizing event was very low compared with that of thermal pro-

cesses, we would expect normal statistical fluctuations in the number of hole-

electron pairs produced. In this case, the RMS fluctuation < n > in the number

of pairs produced would be given by:Ip.

< n > = εv 2(3.1)

where E = energy absorbed by the detector,

ε = average energy required to produce a hole-electron pair.

In semiconductor detectors the situation lies between these two extremes. In

silicon, for example, the yield (i.e., the ratio of the energy used in ioniz-

ing events to the total energy absorbed) is about 1.1:3.6 or about 30%. Fano

*We assume here that the entire particle energy is absorbed in the detectorso that such effects as the Landau collision processes can be neglected.


studied the equivalent situation in gaseous detectors1,2 and the signal spread

is now usually expressed in terms of the Fano factor F. If no is the observed

RMS spread we have:

2-no = F < n >

2(3.2)

In our case, it will be clear from the preceeding discussion that F must be

smaller than unity. Van Roosbroeck has recently performed an elaborate

statistical analysis of the situation. His methods and results are outlined

in the following paragraphs.

A high energy ionizing particle (or the electron produced by a gamma-ray)

produces secondary electrons of lower energy, which produce further lower

energy electrons and so on. Energy losses in this shower process are of three

types:

(a) An electron may impart sufficient energy to an electron in the lattice

to raise it into the conduction band and produce a hole in the lattice.

In this case the original energy is reduced by a small amount equal

to the band-gap of the material and the remainder of the energy is

shared between the degraded incident electron, the secondary electron

and secondary hole. It is usual to assume that the secondary electron

and hole are given equal amounts of energy although this is dependant

upon details of the band structure of the material. The sharing of

energy between the degraded incident electron and the hole-electron

pair can be considered to be random in nature.

(b) An electron travelling through the lattice may lose energy by inter-

actions with the lattice itself. Most of these interactions excite

the lattice in an optical mode of vibration. The energy exchange in

these interactions is quantized and the quanta are characterized by


the Raman frequency of the lattice. For silicon and germanium the

Raman phonon energy is ~ 50 x 10-3 eV and the fact that the ion-

ization yield is only ~ 30% indicates that many optical phonon

collisions take place for each ionizing collision.

(c) The large numbers of very low-energy electrons produced at the

end of the shower process, not having sufficient energy to produce

secondary ionization, must lose the remainder of their energy by

thermal losses to the lattice.

The overall process is shown diagramatically in Fig. 3.1. Using this

model Van Rocsbroeck24 has calculated the curves shown in Fig. 3.2. As the

average energy expended per hole-electron pair finally released is determined

by the same processes as the fluctuations in the number of hole electron pairs,

he has expressed both the yield (i.e., )Energy Gap (Eg)

Average energy per hole electron pair (ε)and the Fano factor as functions of the average number of phonon collisions

per ionizing collision (i.e., r/l-r). If we use the measured values of the

average energy absorbed per hole electron pair we can, by applying Van Roosbroeck's

data, derive a value for the number of phonon collisions per ionizing collision

(~50 for Si, ~90 for Ge) and thence obtain probable values for the Fano

factor (0.28 for Si, 0.36 for Ge).

Unfortunately accurate experimental determination of the Fano factor for

silicon and germanium proves difficult due to several factors. At low energies,

the statistical spread clue to the basic charge production mechanism is usually

small compared with the amplifier noise. This leads to large possible errors

in the determination at low energies. At high energies, many germanium detectors

show poor energy resolution due, we believe, to material non-uniformity. Gamma-

ray measurements at high energies in silicon are difficult due to the very low

efficiency in the photo-peak which makes the measurement doubtful if done with


large activities due to the high counting rate of Compton events and, if done

with small activities, due to amplifier drift, p-particle measurements, on

the other hand, suffer energy loss in the entry window into the detector.

Other complicating factors arise which will not be detailed here. Despite

these difficulties some measurements have been carried out in both silicon

and germanium and the results are consistent with Van Roosbroeck's theory.

A recent set of measurements by Sven Antman and Don Landis in our laboratory

is shown in Fig. 3.3. This shows a plot of the energy resolution (squared)

of a 2 x 1 x 0.8 cm germanium detector as a function of gamma-ray energy.

Great care was taken to eliminate amplifier drift, etc. and the fact that

the points fit well on a straight line indicates that we were dealing with

a purely statistical process. The Fano factor established by these measure-

ments is 0.30 ± 0.03 which is entirely consistent with the approximate value

of 0.32 derived from Van Roosbroeck's curves.

.

3.3 ELECTRICAL NOISE SOURCES

For practical purposes we can assume that all the charge produced in

the detector is collected (i.e., it flows as current in the external circuit).

Therefore, the statistical fluctuations discussed in the previous paragraph

represent the only truly fundamental limits to the energy resolution. However,

several factors prevent our realizing the ultimate resolution in existing

systems. Before outlining these factors it will be useful to discuss a typical

electronic system associated with a semiconductor detector.

Fig. 3.4(A) shows a block diagram of a typical system. The detector supply

voltage is applied through a load resistor, always large in value, so that the

small pulse of charge which flows in the detector in response to the passage

of an ionizing particle will flow into the input of the preamplifier via the

coupling capacitor Cc. After amplification the signal is passed through a


frequency selective filter (often called a pulse shaper) which, in essence,

rejects as much noise while retaining as much signal as possible. A charge

sensitive configuration of the preamplifier as shown in Fig. 3.4(B) is

usually employed as this type of circuit gives an output signal size which,

to a first approximation, is independant of the value of the detector and

stray capacities which appear from its input to ground. This is purely a

matter of convenience and the tradition has grown due to the fact that the

capacity of a junction detector varies as the applied voltage is changed.

The charge sensitive configuration is a little poorer than the conventional

voltage amplifier from the point of view of resolution due to the feedback

capacitor CF behaving as an additional capacity to ground in the equivalent

noise circuit (i.e., a part of CIN in Fig. 3.4(C)).

The equivalent input circuit for studying the energy resolution capabil-

ities of the system is shown in Fig. 3.4(C). The various noise and signal

elements are as follows:

(a) The input signal Q, usually assumed to be a pulse of current of

very short duration compared with the time constants involved in

the system. We will see later that this approximation is not

always valid but will neglect these cases for the moment.

(b) The detector leakage current noise (iN)D. This is assumed to be

pure shot noise which implies that it consists of individual electrons

and holes crossing the depletion layer with no interaction (e.g.,

space charge effects) occurring between the individual carriers.

It arises due to thermal generation of electron-hole pairs in the

depletion layer as expressed in equations 1.13 to 1.15. The mean

square value of the current fluctuations in a leakage current of

Lecture 3 -93-

this nature is given by:-i2 = 2 q · i ∆f.

UCRL-16231

(3.3)

where ∆f is the frequency interval in which the noise is

measured.

(c) The detector series resistance noise (en)RS is due to resistance in

the connections to the sensitive volume of the detector. If the

sheet resistance of the n-type diffusion or the resistance of the

bulk material at the rear of the depletion layer is high this might

be an important source of noise but in well designed detectors it

can be made negligible. We will assume that it is unimportant in

the following discussion. This allows us to simplify the equivalent

circuit by regarding the detector capacity CD and the amplifier input

capacity CIN as being in parallel. We will replace CD + CIN by CT

in the following discussion.

(d) The input current noise (iN)G is due to fluctuations in the input

current to the first amplifying device in the system. If this is a

vacuum tube,it is the sum of the positive and negative grid currents,

assuming that both are present simultaneously. The fluctuations

in this current behave like those in detector leakage current and,

since the two sources in the simplified circuit are in parallel,

we can use equation 3.3 to represent their sum if i = iD + iG.

(e) The parallel resistance noise (en)RL arises from any resistors

shunting the input circuit. This includes the detector load, any

input biasing resistor in the first stage and any resistor included

across CF in a charge sensitive preamplifier. In practice, very

large values are used for these resistors* and we can regard the

time constants used for pulse shaping in the amplifier.

*If RL is the total effective parallel resistance the criterion of interesthere is that the value of the product RL. CT shall be much larger than the


voltage source (en)RL in series with the large resistor RL as a

current source which must also be included in the value of the_

current generator i2 in the previous paragraphs. The increase

in i2 due to this 4 kT ∆f. For this to be negligible we should

_

RL_

make:

(3.4A)

For example, if i = 10-7 A; RL >> 5 x 105 ohm meets the require-

ment. We will assume now that this requirement is satisfied.

(f) The noise developed in the first amplifying device produces a

voltage noise source (en)Req. If this device has adequate gain the

noise due to later amplifier stages is negligible. This source of

noise can be represented by Johnson noise in a resistor and has

the value:

_2en = 4 kT Req ∆f (3.4B)

Where Req is an equivalent input noise resistance in the amplifying

device. In the case of a vacuum tube it is due to fluctuations

in the anode current partially smoothed by the space charge in the

grid-cathode region. Its value is about 2.5_gmfor a triode having a

mutual conductance gm.

Two sources of noise are not shown in Fig. 3.4(C) but must

receive some attention:

(g) Surface leakage currents arising at the periphery of the junction

produce severe low frequency noise in many detectors. The guard-

ring structure and correct surface passivation as described in the

section on diffused detectors in Lecture #2 largely eliminate this

source of noise in many applications. As no adequate theory exists


to explain the details of the behavior of this noise we will

neglect it here.

(h) The plate current of a vacuum tube or other amplifying device shows

fluctuations of a similar nature to those occurring at the surface

of a junction detector. These fluctuations are believed to arise

in processes occurring in the cathode and are dominantly in the low

frequency part of the spectrum.

This source of noise, commonly called "flicker effect" is

usually represented by a noise voltage generator in the input lead

having the value:

(3.4C)

where f is the frequency at which the frequency increment ∆f is

centered and A is a constant (commonly said to be about 10-13).

We can therefore simplify the input circuit for practical purposes to

the one given in Fig. 3.5(A). This can be further simplified to contain only

voltage generators as shown in Fig. 3.5(B). We must now examine the effect

of the amplifier frequency response upon the relative values of signal and

noise at the amplifier output.

3.4 EFFECT OF AMPLIFIER SHAPING NETWORKS

One purpose of the amplifier is the trivial but important one of

amplifying the signal to a level at which it can be used to operate logic

circuits. However, both noise and signal are amplified and frequency dependant

networks must be used to selectively amplify the signals more than the noise.

It will be immediately obvious that a shaping network which results in the

amplifier passing only a narrow range of frequencies will minimize the noise

output power but, unfortunately, it will also reduce the output signal. There-

fore it is reasonable to suppose that the frequency selective network has to be


optimized and the optimum network will depend upon the relative values of

the voltage noise components shown in Fig. 3.5(B). Examination the

noise generators indicates immediately that the noise due to input current

is dominantly low frequency noise, while shot noise in the input element is

more important at high frequencies and flicker noise falls between these

extremes. To determine the actual contributions due to each of these terms

we must evaluate their effect over the full frequency range of the amplifier.

Let F(f) represent the frequency response of the amplifier. The three

contributions to output noise are then:

(a) Shot_ 2EN = 4 kT Req

2

_

(3.5)

(b) Flicker "in+ df (3.6)

(c) Current_

EI = (3.7)

We must now examine typical frequency selective networks to permit evaluation

of the three integrals in (3.5), (3.6) and (3.7). In general, the complete

network will consist of at least one low-pass network (e.g., an RC integrator)

to reduce the shot noise, which would otherwise increase rapidly at high

frequencies, and at least one high-pass network (e.g., an RC differentiator)

which serves to reduce low frequency noise due to input circuit currents.

It will be convenient to express the parameters of the networks in terms of

a normalized frequency fo (and an equivalent time constant to = ). 2 π fo1

Thus, a single RC integrator network of time constant τ, will be represented

by a parameter n, where τ = n τo. The frequency f will be represented by

the parameter m where f = m fo. The gain-frequency function for the RC


integrator shown in Fig. 3.6(A) therefore becomes:

Gain2 = 1 =

1

1 + 4 π2 f2 R2 C2 1 + (nm)2

The gain-frequency function for a number of elements used to build up

shaping networks: expressed in this form, are shown in Fig. 3.6.

In terms of the parameters m and n the equations 3.5, 3.6 and 3.7 can be

rewritten:_EN = 4 kT Req fo 2

?(m1,n1) · F2 (m1,n2) ....) dm (3.8)

EF = A lo?? (F1 (m1,n1) · F2 (m1,n2) ....) ??

m (3.9)

_qi

EI =2

Io. (F1 (m1,n1) · F2 (m1,n2) ...)

m2- dm (3.10)2 π2 CT fo

2

2

_

0

where F1 (m1,n1) represents the frequency response (squared) of the

first element in the shaping network.

F2 (m1,n2) represents the frequency response (squared) of the

second element in the shaping network, etc.

We note now that once a network is chosen (and we assume here that it

is built up of some of the elements shown in Fig. 3.6; elements may be

repeated more than once) the integrals involved in equations (3.8), (3.9) and

(3.10) can be evaluated. We then see that the time scale can be changed

(i.e., fo is changed but n1,n2, etc., remain the same) and only the constants

before the integration signs are affected. Thus the shot noise2 is always

proportional to fo (or inversely to τo), the flicker noise2 is always

*These elements may require a few words of explanation. The RC integratorand RC differentiator require no elaboration. The delay line integrator isa little different from the shorted line frequently employed in amplifiersbut, analytically, it amounts to the same thing. A delayed signal is sub-tracted from the input signal at the input to an operational amplifier stage.The fedback integrator and differentiator are standard operational amplifierconfigurations and, for the purpose of analysis, the open-loop gain of theamplifier is assumed to be infinite.


independant of fo and the input current noise2 is always inversely pro-

portional to fo (or proportional to τo). This is independant of the specific

types of element used in the shaping network.

To illustrate a specific case of equations (3.8), (3.9), and (3.10) we

will look at the shaping network containing a single RC integrator of time

constant τo and a single RC differentiator of time constant to isolated by

a suitable stage τo prevent interaction between the two elements. In this

case equations (3.8), (3.9), and (3.10) become:

2/

Qb

2

EN = 4 kT Req fo

_m2

dmO (1 + m2)2

(3.11)

_2EF = A /

O"m

0 (1 + m2)2dm

_qi 00

EI = 2 s1 dm

2 π2 CT fo 0 (1 + m2)2

These integrals can easily be evaluated analytically and, for this reason,

(3.12)

(3.13)

this case is dealt with in all textbooks. More complex networks containing

several RC integrators, delay line shapers, etc., are analytically quite

unmanageable but the author has recently dealt with a number of such complex

networks by a numerical integration procedure using a computer (see Table 3.1).

The results will be presented shortly.

Hitherto we have concerned ourselves primarily with the effect of these

shaping networks on noise. We must now see what effect they have in the signal.

We mainly interested in the peak height of the output signal as this is the

quantity measured by a pulse-height analyzer. The input signal, as shown in

Fig. 3.5(B), consists, to a first approximation, of a step function of amplitude

The response of a number of typical networks to a unit step function has


been calculated using a digital computer (see Table 3.1) and, for the moment,

we will assume that the output peak pulse height (for unity amplitude input)

is P. Since we are dealing with a linear network the output pulse amplitude

due to the detector signal is then PQ _

CT . In comparing this with the noise we

_must either square the signal or take the square root of the noise2. We will

choose to use the signal squared:

The general equations (3.8), (3.9), and (3.10) can be rewritten:

_EN 4 kT Req CT2 2 _

S2 P2 Q2 = fo ???? (m1,n1) · F2 (m1,n2) ...) dm

???? (m1,n1) · F2 (m1,n2) ...) dm

m

_

=EI qi

J-O”2

S2 2 π2 P2 Q2 fo

_ (F1 (m1,n1) · F2 (m1,n2) ...) dm

_0 m2

(3.14)

(3.15)

(3.16)

It is common to express the noise as the equivalent input noise signal quoted

in ion (or hole-electron) pairs. This implies rewriting equations (3.14),

(3.15) and (3.16) with 1.6 x 10-19 coulombs inserted for Q. To simplify the

presentation we will also substitute I1, I2, and I3 for the three integrals

and will assign values to some of the constants:

(3.17)

(3.18)

(3.19)


We note that the dependance of the three types of noise on the shaping network

is contained in the second terms in parenthesis. The inverse of these ratios,

calculated by a computer for a number of types of netvork, are shown in

Table 3.1. The dependance of noise on the input circuit and on the input

amplifying element is contained in the first terms in parenthesis. The

equivalent shot and flicker noise squared are each proportional to the total

input capacity squared. On the other hand, the equivalent input current noise

squared is independent of the capacity. The overall frequency dependance of

the three types of noise is shown in the terms containing fo.

In Table 3.1 the first four cases involve only RC shaping elements while

the remaining cases use delay-line feedback integrators and simple RC shaping

elements. Comparison of cases #9 and 10 illustrates the worsening of noise

due to double delay-line differentiation. Case #8 is a special one which was

studied mainly from the point of viev of the rather ideal pulse shape it

produces. In all cases, the value in the IP2_ column can be regarded as a figure

of merit of the network for that particular type of noise. Comparing case #5

with case #1 we see that the single delay line with RC integrator is superior

in shot noise ( =P2_ 0.200 as compared with 0.172), flicker noise (0.376 com- I1 -

pared with 0.270) and input current noise (0.34 compared with 0.172.). The useτoof two RC integrators ( )_2 with the delay line (τo) improves shot noise

at a small cost in flicker and input current noise.

However, comparison between networks is not as simple as indicated in

Table 3.1. In many experiments an important factor involved in the choice of

network is the speed of recovery of the shaped waveform to the baseline. This

parameter determines the degree to which pulse pile-up will be a factor at high

counting rates. Fig. 3.7 shows the pulse shapes produced by several of the

networks listed in Table 3.1. We see that, of the cases shown here, the long


tail associated with the RC integrator-differentiator case (#1) is consider-

ably worse than that in the RC integrator-DL differentiator case (#5). The

network #8 is unique among the networks considered here in tha its tail has

completely ended 2.0 µsec after the start of the pulse. Among the more

conventional networks, the double delay line differentiator networks possess

notable advantages at high counting rates. Not only is the tail on the

double delay-line pulse comparatively short but the complete area balance

between positive and negative components of the pulse means that base-line

fluctuations at high rates are small. As seen in cases #9 and #10 of Table 3.1,

however, the price paid for using a double as compared with a single delay line

is an increase in noise.

Another factor influencing the choice between shaping networks is their

sensitivity to input pulse rise-time variations. As will be seen in Lecture 4,

the pulse shape from a practical detector does not have an infinitely short

rise-time and the rise-time depends upon the initial location of the ionization

in the detector. If the maximum collection time is an order of magnitude

smaller than the time constants involved in the shaping network, the effect of

detector rise time variations is negligible but this is not the situation when

using thick silicon and germanium detectors. We have experienced difficulties

in using 3 mm thick silicon detectors for alpha-particles in the energy range

20 - 120 MeV due to the variation of rise-time in the detectors which ranges

from about 100 nsec to 300 nsec depending upon particle energy.* This is in

the same general range as the time constants used in the shaping networks so

that the output amplitude departs from being a linear function of input particle

energy. Moreover, since the particle range is subject to statistical variations,

another source of spread in the amplitude of output signal becomes evident.

In cases where this might happen, the choice of shaping network is influenced

by its sensitivity to input pulse rise-time in addition to the signal to noise

The particles are incident normal to the detector window and therefore theparticle track extends along the lines of electric force.


and counting rate factors discussed earlier. As a general rule, networks

whose output pulse shape has a rounded top (i.e.,_d2V = 0 at Vmax) exhibitdt2

less input pulse shape dependance than networks having a peaked top. It

will be evident from Fig. 3.7 that the single RC integrator delay-line

differentiator #5 (with the delay line length equal to the RC integrator time

constant) is poor in this respect. Using a numerical method the behavior of

several typical networks with regard to input pulse shape sensitivity has

been calculated and the results are given in Table 3.2. This table shows

the percentage loss in pulse height at the output when 40 and 85 MeV alpha-

particles enter a 3 mm silicon detector (at 25°C with 350 V applied to it) as

compared with the pulse height if the detector exhibited an infinitely short

rise time. We note that similar results would be obtained if gamma-rays inter-

acted at various points in the detector.

Examination of Table 3.2 shows, as expected, that the networks which

provide flat-topped pulses perform better with regard to pulse shape sensitiv-

ity. The Table also shows that increasing the time constants of a network to

seperate them further from the input pulse rise time produces a considerable

improvement. However, this increases the input current noise and counting-

rate dependance. The network #9 (which is the same as #8 in Fig. 3.7 and

also #8 in Table 3.1) was designed to produce good input pulse shape dependance

at the same time as good noise and counting rate characteristics. This result

is achieved but the complexity of the arrangement prohibits its general use.

Finally we must note that the fact that the percentage loss figures in Table 3.2

differ for the 40 and 85 MeV particle results in a non-linearity in the energy

calibration of the system. In case #5 this non-linearity amounts to about 2.1%

and had been observed experimentally prior to these computations. A gross

worsening of energy resolution had been observed at the higher energies in these

experiments and both the linearity and resolution effects were largely corrected

by changing to the conditions in Case #8.


3.5 VACUUM TUBES AS THE INPUT AMPLIFYING DEVICE

The optimum choice of vacuum tubes for use as input amplifiers depends

upon the type and properties of the detector being employed. For the purpose

of analysis it is usual to assume that the sources of noise associated with a

vacuum tube are grid current noise (which contributes to the input circuit

noise of equation (3.19)) flicker noise (which contributes to EF in equation

(3.18)) and shot noise (which is responsible for the Req of equation (3.17)).

The grid current and shot noise in a modern vacuum tube are believed to be

well understood theoretically but the flicker effect can differ greatly between

different types of tube and even between individual tubes of one type. There-

fore choice of tube type is made first on the basis of the two best understood

parameters and final selection is usually made by carrying out noise measure-

ments on many samples of the selected types of tubes to determine the amount

of flicker and unexplained noise contributions.

According to Fairstein, the grid current of a triode operated in the normal

mode* is caused primarily by photoelectric emission from the grid due to soft

x-rays produced at the anode by electron bombardment. The grid current is given

approximately by:

Ig = Eg-p IK x 10-10

_

32

where Ig = grid current in amperes,

Eg-p = grid to anode voltage in volts,

IK = cathode current in amperes.

For example, if IK = 12 mA and Eg-p = 100 V; I x 10-9 A.

The grid current of a typical EC-1000 (Phillips) tube operationg under these

conditions is about 2 x 10-9 A which is in satisfactory agreement with Fairstein's

theory.

It is assumed that the grid bias is large enough to prevent electron collectionat the grid.


It is well known that the equivalent noise resistance of a vacuum tube

triode is approximately equal to 2.5/gm where gm is them utual conductance*

expressed in mhos. However, to prevent very high frequency oscillations in

a vacuum tube it is necessary to insert a grid "stopper" resistance in the

grid lead. This must be added to the tube noise resistance to obtain Req in

equation (3.17). For the EC-1000 tube operated under the conditions of the

previous paragraph and with a 22 ohm grid stopper gm ~16 mA/V and Req = 180 ohms.

It will be clear from the previous two paragraphs that a tube which operates

at a low plate voltage and current will produce a small grid current. However,

this will result in a rather low value of mutual conductance. From equations

(3.17) to (3.19) we see that this means that the vacuum tube will contribute

little noise if long time constants are used in the shaping network (i.e., fo

small) and considerable noise for short time constants. If a detector (such as

lithium-drifted germanium at liquid nitrogen temperature) has very little

leakage current and low capacity, use of an input tube having these character-

istics might make good sense. However, the optimum shaping network would have

a long time constant ( ~5 µsec) and the performance at even moderately high

counting rates performance would be very poor. Moreover, many extraneous

sources of noise such as detector surface noise, microphony in the tube, etc.,

tend to increase at low frequencies. In practice it is usually more satisfactory

to try to work with short time constants in the shaping network and to choose

the tube accordingly.

A high-capacity high-leakage detector calls for a tube having the highest

possible mutual conductance. Its high grid current is of little consequence

since it is swamped by the detector leakage current. In this case the optimum

time constant in the shaping network will be in the 0.5 to 1 µsec region. We

use a 7788 for these purposes.

*If this value is to be put into equation (3.17) T must be assumed to be 300°K.


The preamplifer used in our laboratory for the great majority of high

resolution experiments is shown in Fig. 3.8. As a large amount of data has

been accumulated on this preamplifier we will examine its characteristics in

some detail. The input tube's anode couples to the grounded base stage Q1,

and the collector output of Q1 is emitter followed by Q2. The collector load

of Q1 is bootstrapped from the emitter of Q2 via C1 so that the effective load

presented to the collector of Q1 is almost purely capacitive in the frequency

range of interest. The transistor type used for Q1 and Q2 has very low

collector-base capacity to speed up the response at the collector of Q1 as

much as possible. Feedback to make the input stage charge sensitive is taken

from the emitter of Q2 via RF CF to the grid of the input tube. A 0.5 pF test

capacitor feeds a test signal to the input grid when required and the detector

signal couples via Cc to the same point. The output signals from the charge

sensitive loop feed the feedback amplifier stage containing Q3 and Q4 and their

output feeds a similar stage containing Q5 and Q6. The total gain in these two

stages is 8 but this can be reduced by a factor of 3 by switching S1 to the low

gain position.

Fig. 3.9 shows the behavior of the equivalent noise (squared) for a typical

preamplifier of this type used with equal RC integrator and differentiator in

the shaping network. The plot shows the variation in the mean noise squared as

a function of the shaping network time constant τo ( τo = ) of equations 2 π fo

1

(3.17) to (3.19) ) and as a function of the capacity from input to ground. This

simulates the effect on the resolution of detector capacity.

The full lines in Fig. 3.9 are experimentally measured curves while the

dotted lines are calculated contributions (from equations (3.17) to (3.19))

from the three noise sources for a value of CT = 14 pF. The constant A in the

calculation of flicker effect has been chosen* to produce the best match of the

*The value of A which appears to be applicable to this case is about 7 timeslarger than the generally accepted 10-13. All our experience indicates thatthe generally accepted value is too low.


sum of flicker, shot and grid current noise contributions to the experimentally

measured curve for CT = 14 pF. The match is almost perfect, and, if the noise

contributions are calculated for the other values of CT, equally good agreement

is obtained.

From Fig. 3.9 we note that the resolution of a germanium detector -

preamplifier combination in which the detector has a capacity of 6 pF (i.e.,

CT = 20 pF) and very low (< 10-9 A) leakage is best for a time constant of

1.0 µsec and corresponds to slightly over 2 keV FWHM. This is observed experi-

mentally with good small area detectors. In Fig. 3.10, the effect of a slightly

different shaping network is shown. If we add a second RC integrator equal

in time constant to the first one (and to the differentiator), the energy

resolution for the 6 pF detector becomes optimum at a time constant of 0.5 µsec

and is about 1.85 keV. Also, shown at the right hand side of these curves are

some results for delay-line shaping with two equal RC integrators. We see

that the 6 pF detector case gives a little less than 1.8 keV. On the other

hand, we note that, due to the short time constant (0.8 µsec) of the delay-line

differentiator, the performance of the delay-line system is worse than the RC

system (at its optimum point) when higher capacity detectors are used.

A convincing illustration of the validity of the theoretical model is

shown in the comparison between Figs. 3.10 and 3.11. The only difference between

the cases shown in these two figures is that the shunt input resistance (RF in

shunt with RL) is 60 M ohm in Fig. 3.10 and 500 M ohm in Fig. 3.11. This

should theoretically (see section 3.3(e)) change the effective value of the

grid current by 0.8 nA. The improvement at long time constants in Fig. 3.11

is close to this value. The improvement in resolution for the 6 pF detector

case is significant (now 1.7 keV).


For future reference in discussing some of the fast timing possibilities

of detectors, the rise time behavior of this preamplifier is shown in Fig. 3.12.

However, it should be remembered that, if a fast amplifier is used to amplify

the signals from the preamplifier, the noise levels, instead of being those

shown in Figs. 3.9 and 3.10, are determined by the time constants in the fast

amplifier. If it contains a differentiator - integrator combination of 10 nsec

time constant the energy resolution with a 12 pF detector will be in the region

of 15 keV FWHM.

3.5 ALTERNATIVE LOW NOISE AMPLIFYING ELEMENTS

Particularly for low-energy gamma-ray measurements, the energy resolving

capability of a semiconductor detector spectrometer is determined at the present

time by the electrical noise properties of vacuum tubes. While minor improve-

ments (e.g., higher gm and reduced igand capacity) in vacuum tube character-

istics can be anticipated it seems unlikely that radical improvements will.

arise in this area. It is natural, therefore, to inquire into the possibility

of obtaining better performance by using techniques not based upon vacuum tubes.

Ultimately we might hope that the energy resolution will be determined solely

by the statistical process described in section 3.2 and, to accomplish this,

we look for an improvement of about 5:1 in the electronic resolution of these

systems.

A little work has been done on the use of a parametric amplifier system

(Chase and Radeka) and some promising results have been obtained. However,

parametric amplifiers are much more complex than our normal amplifiers in

requiring the use of a very high frequency radio frequency carrier. As a

consequence the behavior of such systems is difficult to analyze and, moreover,

obtaining the ultimate performance depends upon critical aajustment of parameters.

Probably for these reasons, no significant results have yet been published on

systems of this type.


A more promising alternative at the present time seems to be the use of

a bulk* field-effect transistor. The operation of this device is illustrated

in Fig. 3.13 which shows a source and drain electrode connected by an n-type

"channel" which is partially "pinched off" by the depletion layer produced

by a reverse biased "p" region diffused into the side of the n-type channel.

(Note that p-type channel devices are also available.) From our previous

discussion it will be obvious that increasing the negative bias on the gate

electrode of Fig. 3.13 causes the thickness of the conducting channel to be

reduced thereby modulating its impedance. Moreover we note that the impedance

seen looking into the gate electrode is very large - being that of a reverse

biased diode. Due to the voltage drop along the length L of the channel the

junction is reverse biased to a greater extent near the drain electrode and

the voltage distribution along its length has the general form shown in

Fig. 3.13. We will only discuss certain aspects of the theory of field-effect

transistors here but the behavior of the device is well understood and has

been thoroughly analyzed.

For some time we have been using field-effect transistors of this type

in a general purpose preamplifier not used for very high resolution work.

Fig. 3.14 shows the circuit of this unit and will be used to illustrate the

mode of use of a field-effect transistor before we examine some of its noise

characteristics, which are of major importance to us in high resolution spec-

trometry. Comparing this unit with the vacuum tube preamplifier we see that

the basic configuration of the input charge sensitive stage containing Q1, Q2,

Q3 and Q4 is similar to that of the stage containing input tube, Q1, and Q2

in Fig. 3.8. However, due to the low voltages required for the field effect

transistor we are able to conveniently D.C. couple the complete loop. Also,

*We have delibertely used the word bulk to discriminate between this type of fieldeffect transistor in which control of carriers takes place in the bulk materialand the type (MOS) in which the conductivity of a surface layer under an oxide ismodulated. Since conduction in a surface layer will most likely be noisy (thisis confirmed by experiment) we will neglect the MOS type of transistor in thisdiscussion.


owing to the rather low mutual conductance (4 mA/V) of the field-effect

transistor, we have found it necessary to use a White emitter-follower Q3,

Q4 within the feedback loop to raise its gain and thereby improve the rise

time. Only a single gain stage is used at the output of this preamplifier;

this is due to the particular area of use aimed for in the design. We should

note two features concerning the input circuit of this preamplifier. The

diode CR1 is provided to protect the transistor against high voltage surges

introduced when switching detector voltage on or off. The adjustable feed-

back and test capacitor arrangements are used to align many preamplifiers

to have the same energy calibration and, in fact, in the particular installation

using these preamplifiers, a Helical potentiometer pulser dial is calibrated

directly in MeV (100 MeV = 1 V into the test capacitor).

According to the analysis of Van der Ziel,25,26 the noise introduced by

a field-effect transistor is due simply to resistance noise occurring in seg-

ments of the conducting channel. A noise voltage developed in a small element

of the channel modulates its width and thereby affects the channel conductance.

Also, the noise modulation of the depletion layer width causes a noise current

to flow in the gate electrode circuit. These effects can conveniently be

expressed for all practical purposes in an equivalent noise resistance Req

given by:

(3.20)

where CT is the total input shunt capacity (as always).

Cgs is the gate-source capacitance of the FET.

Equations (3.17) to (3.19) are still valid for this case, where Req in equation

(3.17) is assigned the value calculated from equation (3.20); constant A in

equation (3.18) is the flicker noise constant (not known for FET's but probably

quite variable from unit to unit due to surface effects at the edge of the

junction); i is the gate junction leakage current.


In choosing a field-effect transistor for use as an input amplifying

element the same considerations apply as in the vacuum tube case. Since, in

most practical situations detector leakage current noise and surface noise

cause noise at long time constants, the objective should be to design for an

optimum shaping network with a time constant close to 1 µsec. This places

emphasis on keeping Req small and, therefore, gm large. Commercial units are

available in the range 2 mA/V to 20 mA/V and these justify examination.*

Assuming a slightly worse value of Req than equation (3.20) would indicate

and a typical total capacity of 20 pF, Fig. 3.15 shows the noise behavior

predicted for gate junction leakage current noise (assuming 10-9 A which is

typical) and for channel noise for different values of gm for room temperature

operation. We have shown no flicker noise contribution in these curves but

recognize that, in practice, such a contribution may be dominant. For a

transistor having a gm of 5 mA/V and ig = 10-9 A the FWHM resolution indicated

by Fig. 3.15 is 1.6 keV with an optimum time constant of 2 µsec. If the mutual

conductance is 10 mA/V the optimum moves to 1.3 µsec and the resolution becomes

1.3 keV.

While recognizing that practical devices rarely agree precisely with

theory, it is extremely promising when theory predicts such attractive results.

However the situation improves still further when we look at the theoretical

behavior at liquid nitrogen temperature. At low temperatures one might expect

flicker noise to disappear** and this removes an important unknown trom the

theory. Moreover, in equation (3.17) we note that the absolute tempearture T

*We note that, if CT = Cgs (i.e., no added capacity) then Req < 1/gm. This isto be compared with 2.5/gm for a triode, a 2.5:1 improvement for the same gm.On the other hand, a low gm in the first amplifying element may cause noisein the second element to become important.

**One can argue that we see no flicker noise in very large area germanium detectorsat 77°K and, therefore, can expect even less from the minute field-effectdevice gate junction.


appears and, unlike the vacuum tube case, we can use low temperatures to

reduce this source of noise. Furthermore, the gate junction leakage current

fails practically to zero and input current noise will be solely that due to

generation of carriers in the bulk of the detector, Fig. 3.16 shows the

predicted behavior of channel noise and input current noise at 77°K. We see

that a gm of 10 mA/V and detector leakage of 2 x 10-10 A gives optimum

resolution of 0.6 keV at 1.5 µsec time constant.

It is interesting to note that it is, in principle, very simple to make

high mutual conductance field-effect transistors for operation at liquid

nitrogen temperature. Since, at this temperature, the donors (or acceptors

except indium) are fully ionized, the behavior of the depletion layer as a

function of gate voltage is unchanged as compared with room temperature oper-

ation. However, the channel conductivity in good material will be ~30 times

larger at 77°K than at 300°K due to the increase in carrier mobility. Both

the gm and the device current will increase by this factor. If the power

dissipated by the device can be removed while maintaining it close to 77°K a

high value of gm should be available. Alternatively, if the current is main-

tained constant while cooling the device, the depletion layer adjusts itself

to thin down the channel and the gate-source capacitance is reduced --

another desirable result.

Measurements of commercial device parameters at low temperatures prove

to be disappointing. Nearly all these devices are manufactured with a highly-

doped poor quality epitaxial channel and impurity scattering limits the improve-

ment in gm to a factor of about 3 as compared with room temperature operation.

Moreover, one suspects that the impurity scattering and trapping processes in

the channel introduce aacitional noise sources. Due to this we are in the

process of making our own FET using materials and techniques similar to those


employed in diffused detectors. However, with all their drawbacks, commercial

field-effect transistors do perform as reasonably low-noise amplifiers and

we present here some measurements on these devices.

The circuits used in these measurements are shown in Fig. 3.17. The upper

circuit is used for testing n-channel devices while the lower one tests p-

channel units. The designs are similar to that of Fig. 3.14 and employ the

same output stage. Choice of resistor R in Fig. 3.17 permits adjustment of

the current in the field-effect transistor over a wide range. In interpreting

the results to be presented here, the fact that only a small number of samples

were tested should be borne in mind. This may explain the apparently inferior

27,28results compared with those given in two published papers. However, the results

given here do represent nearly the best obtained from a lengthy investigation of

several promising types of commercial field-effect transistors.

Fig. 3.18 shows performance curves for a p-channel unit (TIS-05) made by

Texas Instruments. This transistor has an effective gate-source capacitance of

about 10 pF and a mutual conductance at 25°C of 4 mA/V. In these tests it was

operated with a source-drain voltage of 4.5 volts. Three samples were tested,

all gave virtually the same results. Previous tests had shown that the con-

ductance of the channel increased by a factor of three at the lower test temper-

ature (about -160°C) as compared with room temperature. Consequently the low

temperature test was carried out at a drain current of 15 mA while the room

temperature test was at 5 mA.

For this type of transistor we note that a large flicker noise contribution

is present at room temperature as indicated by the flatness of the curves. We_

also see that the value of N2 at low temperatures is almost an order of magni-

tude higher than would be predicted from Fig. 3.16. However, at time constants

greater than 1 µsec the low temperature performance of this type of unit is

better than the results obtained with the EC-1000 for the low capacity conditions.

these extra sources of noise is best illustrated by the fact that our tests

on some samples of one type of transistor show that its noise level increases

as the temperature is reduced. There is good evidence that a field-effect

transistor made with good material will come close to theoretical predicted

performance.


Fig. 3.19 shows the results of a similar set of measurements on the

Amelco 2N3458. We note again that the results for N2 are almost an order

of magnitude larger than predicted despite the fact that these units are

apparently largely free of flicker noise. The higher gate source capacity

of these units partially accounts for the results on the Amelco device

being worse than those on the TI unit.

In conclusion it might be said that commercial field-effect transistors

made by the epitaxial process almost equal the best vacuum tube performance

in low noise preamplifiers but unexplained sources of noise prevent them

approaching their theoretical possibilities. The lack of understanding of

3.7 ADDITIONAL SOURCES OF SIGNAL AMPLITUDE SPREAD

The previous sections have been-concerned with rather fundamental sources

of spread in the amplitude of signals. However, it is frequently the case that,

due to the nature of the experiment or due to inadequate appreciation of the

problems on the part of the experimenter, the forementioned sources of signal

spread are swamped by other problems. We will briefly discuss a few of these

problems here.

3.7.1 Noise Contribution of Main Amplifier.

Nearly all amplifier systems contain a signal attenuator to permit oper-

ation with large input signals as well as small ones. This usually appears

between the preamplifier and the first amplifying stage of the main amplifier.


If large signals are produced at the input to the preamplifier, the attenuation

must be increased to maintain the amplifier in its linear working range. This

is always the case when dealing with high energy reactions using silicon

detectors. In these cases one must be careful to avoid the noise in the first

amplifying stage of the main amplifier becoming dominant. For this reason it

is usually necessary to provide a further gain attenuator switch located later

in the amplifying chain and this should be turned to its lowest gain

position before attenuating at the input to the main amplifier.

3.7.2 Gain Drifts

In high resolution spectroscopy using semiconductor detectors one is

frequently working with a spread in the amplitude of pulses equal to about

0.1% of their value. Gain drifts in amplifying systems over a period of a few

hours may well be in the region of this same percentage. The experimenter

must use either a very stable amplifier or one equipped with an overall gain

stabilization servo system if he is to use the true potential resolution of

semiconductor detector systems. This is particularly true when using silicon

detectors for high energy nuclear reaction studies in the 10 to 100 MeV range

and in the case of measurements of high energy gamma-rays ( ~ 1 MeV or greater)

with germanium detectors.

3.7.3 High Counting Rates

At high counting rates pulse pile-up and baseline fluctuations may cause

serious signal spread. It is a good rule to anticipate trouble from this

source if the counting rate is higher than p/τo, where p is the fractional

resolution in the detector amplifier system. Thus if p = 0.3% and τo = 1 µsec,

one begins to detect rate effects at about 3 kc/s. The counting rate at which

these effects appear can be increased by an order of magnitude or more by using


double delay-line or double RC differentiation but use of this type of shaping

network causes a loss of resolution at low counting rates (compare cases #9

and #10 of Table 3.1).

3.7.4 Finite Detector Pulse Rise Time

Since the detector pulse shape is a function of the position of formation

of ionization in the detector, a spread in detector pulse shape results in

many detector applications. If the detector pulse rise time is within a factor

of 5 of the value of to used in the shaping networks, a spread in signal

amplitude at the output of the amplifier can be anticipated. Table 3.2 gives

some guidance toward choice of network in these cases and the section dealing

with detector pulse shape in Lecture #4 also presents some information relevant

to this situation.


Table 3.1. Noise Integral and Peak Response of Several Networks

PEAKOUTPUT (P)

NETWORK DESCRIPTION (UNITY INPUT)

1. RC INTEG (τo) .368 .784 .172 .500 .270 .785 .172+RC DIFF (τo)

2. TWO RC INTEG (τo) .271 .196 .372 .250 .292 .589 .124+RC DIFF (τo)

3. THREE RC INTEG (τo/2) .356 .407 .310 .421 .300 .771 .163+RC DIFF (τo)

4. RC INTEG (τo)TWO RC INTEG (τo/2) .295 .233 .373 .290 .300 .640 .136RC DIFF (τo)

5. RC INTEG (τo) .628 1.98 .200 1.05 .376 1.16 .341D.L. DIFF (τo)

6. TWO RC INTEG (τo/2) .631 1.87 .214 1.20 .333 1.32 .303D.L. DIFF (τo)

7. RC INTEG (τo)TWO RC INTEG (τo/2) .388 .494 .303 .481 .312 .823 .182D.L. DIFF

8. TWO F.B. INTEG (τo)TWO D.L. DIFF (τo) 1.000 4.19 .239 3.61 .277 4.82 .208TWO D.L. DIFF (2 τo)

9. RC INTEG (0.4 τo) 0.981 7.70 .125 3.77 .254 3.79 .253 D.L. DIFF (1.6 τo)

10. RC INTEG (0.4 τo) 0.981 23.0 .042 9.82 .098 6.37 .151TWO D.L. DIFF (1.6 τo)


Table 3.2. Input Pulse Shape Dependance of Several Shaping Networks

(3 mm Li-drift Si detector at 350 V and 25°C)

PERCENTAGE LOSS FOR PERCENTAGE LOSS FOR40 MeV ALPHAS 85 MeV Alphas

1. RC INTEG (0.5 µsec) 0.46 1.73 RC DIFF (0.5 µsec)

2. RC INTEG (1.0 µsec) 0.11 0.41RC DIFF (1.0 µsec)

3. THREE RC INTEG (0.2 µsec) 0.54 1.96RC DIFF (0.5 µsec)

4. THREE RC INTEG (0.2 µsec) 0.99 3.01D.L. DIFF (0.8 µsec)

5. RC INTEG (0.5 µsec) 3.11 5.22D.L. DIFF (0.8 µsec)

6. RC INTEG (0.5 µsec) 3.59 5.74TWO D.L. DIFF (0.8 µsec)



9. TWO F.B. INTEG (0.5 µsec) TWO D.L. DIFF (0.5 µsec) 0.46 1.57D.L. DIFF (1.0 µsec)

Fig. 3.1 Diagramatic Representation of Energy Loss Process.

Fig. 3.2 Calculated Yield and Fano Factor.

Fig. 3.3 Resolution-Energy Relationship Data for Germanium.

Fig. 3.4 Typical Electronics for Spectroscopy.

Fig. 3.5 Simplified Input Equivalent Circuits.

Fig. 3.6 Typical Shaping Networks and Their Frequency Response.

Fig. 3.7 Pulse Response of Several Networks (Unit Function Input).

Fig. 3.8 EC-1000 Preamplifier.

Fig. 3.9 Noise Performance Curves for EC-1000 Preamplifier.

Fig. 3.10 EC-1000 Preamplifier: Effect of Double Integrator.

Fig. 3.11 EC-1000 Preamplifier. (Conditions as in Fig. 3.10 except

Fig. 3.12 EC-1000 Preamplifier Rise Time Curves.

Fig. 3.13 Bulk Field Effect Transistor (N-Channel Type Illustrated).

Fig. 3.14 General Purpose Field Effect Transistor Preamplifier.

Fig. 3.15 Predicted Noise Behavior of Field Effect Transistor at 300°K.

Fig. 3.16 Predicted Noise Behavior of Field Effect Transistor at 77°K.

Fig. 3.17 Circuit for Low Temperature Tests on Field Effect Transistors.

Fig. 3.18 Noise Performance of TIS-05 Field Effect Transistor.

Fig. 3.19 Noise Performance of Amelco 2N3458 Field Effect Transistor.

-118- UCRL-16231


[ ]er = Raman Phonon Energy for Lattice.

eg = Band-Cap of Materialp Assumes a Random Value in the Range 0 to 1.

(RF = 60 M Ω)

RF = 500 M Ω)

(2N3458 at Room Temperature.)

CT = 20 pF; Req = 1/gm Assumed

CT = 20 pF; Req = 1/gm Assumed

Conditions: See Text; Dotted Lines: -170°CFull Lines: + 25°C

Conditions: Dotted lines: -170°C ID = 12.5 mAFull lines: + 25°C ID = 5 mA

-138- UCRL-16231

LECTURE 4. MISCELLANEOUS DETECTOR TOPICS

Fred S. Goulding


July 30, 1965

4.1 DETECTOR PULSE SHAPE

The passage of an ionizing particle or the interaction of a gamma-ray in

the sensitive region of a detector releases a large number of hole-electron

pairs which are separated and collected by the electric field present in the

depleted region. The initial spatial distribution of the hole-electron pairs

depends upon the type and energy of the radiation and, therefore, the shape of

the current pulse obtained from the detector is changed by the same factors.

It is also determined by the thickness of the sensitive region, by the electric

field distribution within this region and by the mobilities of the charge

carriers in the semiconductor at its operating temperature. The interrelation

between these factors makes a general solution to the calculations of pulse

shape quite impossible. We will therefore content ourselves with discussing

some of the basic considerations and giving some examples of solutions for

particular cases. It is instructive to first consider the signal resulting

from creation of a single hole-electron pair in the sensitive volume. As the

result is different for p-i-n detectors, in which the electric field is constant

through the whole sensitive region, from that for p-n junctions, in which the

field is a linear function of distance from the back of the depletion layer,

we will deal with these two cases separately.

Lecture 4 UCRL-16231

4.1.1 Pulse Shape Due to a Single Hole-Electron Pair in a P-I-N Detector

We will consider the situation depicted in Fig. 4.1. The parameters shown

in this figure are self-explanatory and will be used here. We will assume that

the detector is connected to a charge sensitive preamplifier with a feedback

capacitor CF and an open loop gain -A, which is very large. Any chrage flowing

in the detector tends to produce a negative signal et the input to the amplifier

but the feedback via CF forces the amplifier input point (and therefore the

detector anode) to stay almost at constant potential. The simplest way to

calculate the signal is to consider the energy balance in the system. Thus,

as the carriers are collected by the electric field in the detector, energy is

dissipated* and, to maintain the energy stored in the detector dielectric, a

charge must flow into the positive side of the detector from the external

circuit. This charge flows almost entirely out of CF giving a negative output

signal from the amplifier.

We have:

1 Q2Energy W stored in the dielectric = 2 C

__

where Q = charge on the detector capacity C.

...

...

V2Also work done on the electron in time dt = Force X Distance = · q · µe.

_ _

_W2

From this:

dW V2 = · q · µedt W2

= Q2 · q· µe

W2C2_

Q dQC dt W2C2

= Q2 · q µe

i.e., dQ V= · q · µe

_ _ _

_ _dt W2

*This energy appears as thermal vibrations in the lattice due to theelectron wave interacting with the lattice.


This is the current ie in the external circuit.

W2V _ .

.. ie = · q · µe (4.1)

This current persists until the electron reaches the positive plate when

it suddenly becomes zero. The time Te taken for this to happen is given by:

_ _ µe V

Te = W-xo W

(4.2)

Similar equations can be derived for the signal due to hole flow:

Vih = · q µh

_

W2

W

(4.3)

Th = ·xo_ _µh V

(4.4)

The total charge flow in the external circuit is given by:

QTOTAL =

= q.

While this is anticipated, the author must comment that many beginners in this

field find it difficult to believe that the total charge flow is not 2 q.

We note that the output signal is the integrated value of i flowing in

the capacitor CF. The resulting output signal due to the hole-electron pair

is shown in Fig. 4.2 (the signal is inverted for convenience). The two compon-

ents of the signal are shown and it will be obvious from this diagram that,

for this type of detector, the signal due to either type of carrier is pro-

portional to the fraction of the sensitive region crossed by that carrier.

This simple situation results from the fact that the net charge residing in

the sensitive region is zero end, therefore, the electric field is constant.

We will shortly see that the situation is more complicated in the case of the


p-n junction detector. A complication arises in the foregoing analysis (and

for p-n junction detectors) if the electric field is large enough to produce

carrier velocities in the same range as thermal velocities of electrons in

the lattice. This is about 107 cm/sec. In germanium, the velocity of an

electron moving through the lattice is limited to about 107 cm/sec.16 and a

similar, though not so abrupt, limiting velocity exists for holes. In silicon,

the velocity of carriers does not saturate as in germanium but the mobility

falls fairly rapidly when carrier velocities reach the region of 107 cm/sec.

This limitation is of some significance when considering very fast timing

with thin (silicon) detectors and also when dealing with the case of germanium

detectors used at 77°K. The high mobility of carriers in germanium at this

temperature means that the saturation velocity is reached for electric fields

in the 1000 V/cm range. This is not an unusual field in germanium detectors

and the previous analysis must be applied with care to this case.

4.1.2 Pulse Shape Due to a Single Hole-Electron Pair in a p-n Junction Detector.

Fig. 4.3 depicts the situation here. The electric field is a linear

function of distance from the bask of the depletion layer. Again we will con-

sider the energy balance equations.

We have:_ _= ·_dWe Qdt C dt

dQe

For the electron:

W22V_ = E(x) µe = · x · µe

dx _dt

2 V µe t_W2

... x = xo e (4.5)


The work done on the electron in time dt:

( )= 4 V2

· q µe x2 dt

dt W4

_

= E(x) 2 · q · µe dt

W4

dWe_ _

... =

4 V2 · q · µe · x

2.?? ??? ???

Equating the two expressions for dWe/dt we have:

= ie = 4 V · q · µe x

2dQe _ _ W4dt

Substituting from (4.5):

4 V · q · µe xo 2 _ 4 µe · V · t

ie = W2

W4 e

The total charge flow due to electrons is therefore:

(4.6)

J-t

Qe = 0

ie dt

(4.7)

The electron is collected after a time Te given by:

W2Te = loge ( )

2 V µe

_Wxo

Substituting in (4.7), the total charge Qeo due to the electron is given by:

Qeo =

(4.9)


For the hole we have:

Also,

dxdt

= E (x ph = - · x · µh)_

dQdt_ = ih = · q · µh x

2_W4 4 V

... ih =

4 V · q · µh · xo _

e W2

W4

2

tih dt.

1 - e

(4.10)

(4.11)

(4.12)

Equation (4.12) shows that the hole collection waveform is a negative

exponential and requires an infinite time to be completed. The time constant

2 VW2

We have

_

Total charge due to hole = Qho = o_

W2 (4.13)

... Total charge (electrons + holes) = q

This is expected.

Fig. 4.4 shows the pulse shape which is produced. We see that this is

much more complicated than the p-i-n detector case and practical use of these


equations is very limited. However, it is interesting to calculate the time

constantW2

4 V · µh for a silicon detector made from p-type material.

We have:

W = 0.33 ex 10-4 µh * 500 cm

2/V sec.

... Hole collection time constant = x 10-9 sec_

ρ

2000ρ= n sec _

2000 (4.14)

If ρ = 1000 Ω cm

Hole T.C. = 0.5 nsec.

The electron component in the output signal is much faster than this. These

results indicate the possible uses of such detetors for fast timing applications.

The very fast apparent charge collection time in a p-n junction detector

introduces the possibility that other factors limit the rise time of the

output signal. For example, the dense plasma of holes and electrons produced

by a heavily ionizing particle must be eroded away partly by self-diffusion

before the holes and electrons can be considered to be moving under the influ-

ence of the applied electric field. The significance of this is indicated by

the fact that a fission fragment track might contain 1018 hole-electron pairs

per cm3 immediately after its formation and this is about five orders of magni-

tude higher than the equilibrium density of acceptors in the material. A

similar situation, though not so exaggerated, exists for alpha particles. It

is very likely that the ultimate timing possibilities of such semiconductor

detectors will be limited by factors like this but insufficient evidence exists

at the present time to determine the limit set by plasma erosion.

Another degradation of output signal occurs due to the series R, shunt

capacity time constant of the detector. If the detector is made with good


low sheet resistance n+ and p+ layers on front and back and is operated

in a punched-through mode this is not an important factor.* However, if

the detector volume is only partly depleted, the series resistance of the

undepleted bulk may be a serious factor in limiting the speed. As an

illustration we might consider a detector made with 500 Ω cm silicon

(p-type) on a wafer thickness of 500 microns but depleted only to a depth

of 100 microns. If the detector is of 1 cm2 area, its capacity will be

about 100 pF and the resistance of the 400 microns of undepleted bulk

material will be 20 ohms. The resulting RC time constant is 2 nsec. The

time constant for hole-collection in this detector is only 0.25 nsec -

showing that rise time in a case like this may be limited by the combination

of detector capacity and series resistance.

Two further possible limitations can be discussed using the example

of the previous paragraph. We will suppose now that the wafer had been

thinner so that the undepleted bulk was negligible. It is necessary to

apply 200 Volts to this detector to deplete 100 microns. The peak electric

field is 4 x 104 V/cm and, assuming a hole mobility of 500 cm2/V sec., the

hole velocity should reach 2 x 107 cm/sec. We note that the peak field is

in the range where junction non-uniformity may cause small avalanching

effects (called microplasma) making the device noisy. Moreover, the calcu-

lated hole velocity is larger than the 107 cm/sec at which the mobility

falls off. The result of this is to slow down the hole collection somewhat.

However, the effect is a minor one as the holes spend most of their time

in the regions of lower electric field where normal mobility may be assumed.

For very fast timing purposes a punch-through device made on high resis-tivity material is best. By applying a large over-voltage the electricfield becomes constant across the device. We note that a carrier travelingat 2 x 107 cm/sec (a good value for the saturation velocity) crosses a25 micron region in 0.1 nsec.


We see that the pulse shape obtained by collection of a single hole-

electron pair in a p-n junction detector is quite complex and, moreover,

the collection times are so short in thin sensitive regions that secondary

effects often determine the output pulse shape. There is therefore little

point in extending the topic of p-n junction detectors to deal with the

complications which arise when collecting a track of ionization. However,

the problem is more manageable and important in the p-i-n detector and we

will now examine it for some types of radiation.

4.1.3 Pulse Shape Distribution for Gamma-rays in Germanium P-I-N

Detectors at 77°K.

Gamma-rays in the energy range of commonest interest may be considered

to possess a low probability of interacting in a germanium detector. More-

over, if the detector's linear dimensions are about 1 cm, the range of the

electrons produced by the gamma-ray is small compared with the sensitive

thickness of the detector (at 1 MeV the electron range in germanium is less

than 1 mm). Therefore we may consider gamma-rays in this energy range to

produce a uniform distribution of events in the detector volume and the

ionization due to each event to be localized at a point. These arguments

must not be applied to the case of low-energy gamma-rays where the absorb-

tion in the front region shields the beck regions giving a non-uniform event

distribution, nor can they be applied to very high-energy gamma-rays where

the range of electrons produced by the gamma-rays is a large fraction of the

detector dimensions. These restrictions limit the validity of this discuss-

ion to the energy range of about 100 keV to 2 MeV.

Since we can now regard the ionization produced by an interaction as

being localized at a point, a pulse shape like that in Fig. 4.2 will apply


to a single event uith the vertical scale being multiplied by the ratio

E/ε. The relative electron and hole contributions to the total signal

will depend upon the exact location of the event in the detector. How-

ever, in Fig. 4.2 the hole mobility was assumed to be much smaller than

the electron mobility. As seen in Fig. 1.2, the calculated hole mobility

at 77°K is slightly higher than the calculated electron mobility. In

practice, due to the velocity saturation phenomena in germanium at field

strengths in excess of 1000 V/cm (which is commonly used for detectors),

it appears that one can assume that both carriers travel at 1.5 x 107 cms/sec.*

Therefore, if an ionizing event occurs at distance xo from the negative

electrode the range of pulse shapes will be as shown in Fig. 4.5. We

note that the fastest pulse occurs when the event is at the middle of the

sensitive region. Moreover, since we are assuming an equal probability of

an event occuring at any position, pulse shapes in the range shown in

Fig. 4.5 are equally probable.

The spread in pulse shape indicated by Fig. 4.5 has two possible con-

sequences. From the point of view of energy measurements, it may cause

a spread in pulse height following the shaping network of the amplifier

(see section 3.4). Present limitations on the thickness of germanium

detectors ( ~ 1 cm) which limits the maximum collection time to aoout

60 nsec and use of typical shaping network time constants in the 1 psec

region have made this an unimportant ractor up to the present time. How-

ever, as thicker detectors are developed it may become significant and,

if so, the effect (which is amenable to calculation) will influence the

choice of optimum shaping network. A more important consequence of the

spread in pulse shape, at the present time, is its effect on the fast

*This value appears to be the best fit to data we have obtained as wellas being close to that measured by Prior.16

Lecture 4 -148-

timing possibilities of germanium detectors. Here a timing pulse is

obtained when the pulse crosses a fixed threshold level. The relative

probability of the delay between the gamma-ray and the timing pulse

having a value t is easy to calculate for the shape distribution of

Fig. 4.5 and is shown in Fig. 4.6. Here the factor β is the setting

of the threshold pulse discriminator expressed as a fraction of the

total pulse height. We see that the distribution of time delays is

characterized by a sharp peak obtained from events in the central region

of the detector and a flat distribution due to the events in the outer

regions. In most practical. applications a range of gamma-ray energies

occurs resulting in a further time spread. However, we have used 3 mm

thick germanium detectors observing two gamma-ray lines (70 and 80 keV)

with a fast coincidence resolving time between the detectors of less

than 5 nsec (FWHM).

In the foregoing discussion we have made the assumption that the

sensitive region of the detector was completely intrinsic so the electric

field was constant through the whole volume. If this is not true, further

time spread may occur. In practice many detectors appear to contain sub-

stantial regions which are poorly compensated.* These regions cause many

very slow pulses which degrade energy spectra as well as coincidence

resolution. T. K. Alexander17 has used a shape discrimination system to

eliminate these slow pulses.

We tend to attribute this to the presence of impurities such as iron,nickel, etc. in germanium. The lithium compensates the acceptors dueto these atoms at the drifting temperatures but these impurity atomsdeionize well above 77°K resulting in overcompensated regions.


_

4.1.4 Pulse Shape Distribution for Protons and Alpha Particles

Stopping in a Lithium-Drifted Silicon Detector.

This is a case where detector pulse shape can seriously influence

energy resolution and it is important to be able to determine the pulse

shape to evaluate its effect. We will consider here the pulse shape due

to absorbtion of alpha-particles in the range 40-90 MeV incident normal

to the surface gold layer of a lithium-drifted silicon detector. Ion-

ization is produced along the entire track but its highest density is

toward the end of the particle's range. The detector output signal will

consist of the integral of a large number of pulse shapes like that of

Fig. 4.2. No analytical solution is available for this problem. However,

the author has carried out a numerical computation on a digital computer

and Fig. 4.7 shows the results of the calculation for alpha-

particles in a 3 mm thick lithium-drifted silicon detector with 350 V

applied to it (at 25°C). This calculation is performed by dividing the

detector into slices .010 cm thick, calculating the energy absorbtion in

each slice using a relationship of the form Range = constant x E1.73, and

finally integrating the signals due to each slice. A similar method can

be applied to other particles.

In the particular case shown in Fig. 4.7 the change in rise time which

occurs for different energies causes a non-linearity in the overall energy

response of the detector-amplifier combination (see Table 1.2). Moreover,

the worsening of energy resolution observed in experiments at energies where

the particles only just stop in the detector indicates that a statistical

process involved in the length of the particle track produces rise-time


variations which thereby cause a spread in pulse height ac the output of

the amplifier system.

4.2 RADIATION DAMAGE IN DETCTORS

Except in the case of some minor applications of detectors as radia-

tion dosimeters the only useful interactions between radiation and the

detector material are those producing hole-electron pairs in the material.

In this case the normal equilibrium of the material is restored in a very

short time and we use only the transient effect for measurements. However,

radiation in its many forms can interact with atoms in the lattice structure

and displace them from their lattice sites. Each such interaction produces

at least one vacancy and an interstitial atom in the lattice. This

vacancy-interstitial pair is known as a Frenkel pair or Frenkel defect.

In general, the atom ejected from its lattice site carries enough energy

to displace further atoms and more than one Frenkel pair is produced by

an interaction. The quantity of defects produced by a single interaction

and the probability of occurrence of a damaging interaction depends upon

the type and energy of the radiation. Dearnaley treats this problem in

some detail in his book18 and we will use his results in this discussion.

4.2.1 Damage Mechanism

The discussion which follows will deal with collisions between an

incoming particle and the semiconductor atoms. Gamma-rays interact in the

material to produce electrons with energies ranging up to the gamma-ray

energy and, therefore, the damage caused is similar to that of fast electrons.

Different types of particles react (with the atoms which constitute the

lattice) in different ways and this causes the amount and character of the

damage to differ considerably. Fast neutrons have very low probability of


producing direct hits with silicon* atoms but the average energy acquired

by the silicon atoms from the collisions is quite high. The resulting

energetic silicon atom produces many secondary defects and the overall

damage to the material is characterized by small highly damaged regions

separated by considerable amounts of undamaged material. In contrast to

this, heavy charged particles interact with silicon atoms by Rutherford

scattering (mutual electrical repulsion) so there are large numbers of

low energy exchanges and very few silicon atoms acquire high enough

energies to produce substantial numbers of secondary defects. Damage by

fast electrons is influenced largely by the fact that a silicon atom can

acquire little energy when an electron collides with it. Therefore damage

is limited almost entirely to the few silicon atoms which acquire suffi-

cient energy to be displaced from the lattice. For low electron energies

(< 250 keV in Si; < 600 keV in Ge) no collision can give sufficient energy

to a lattice atom to displace it. Measurements of the energy required to

displace a silicon atom indicate that 25 to 30 eV is necessary.

The case of slow neutron damage is a little different from those

discussed above. Here the capture of a neutron by Si30 (4% of silicon)

produces P31 and a β-particle whose energy ranges up to 1.5 MeV. Damage

of the Frenkel defect type is produced by the electrons as in the previous

paragraph. However, the phosphorous atoms now act as donors in the lattice

and the bulk resistivity changes. This can be considered to be damage or a

desirable result depending upon its effect on detector performance.**

Fortunately the cross-section for this process is small.

We will deal only with silicon in this discussion. Radiation damage ingermanium detectors used only for gamma-rays appears likely to be small.However, germanium detectors will be very susceptible to damage if used in asignificant flux of neutrons. The effects of the damage may not be evident,however, as long as the detector is maintained at a low temperature wherediffusion of lithium and vacancies is negligible.

**The production of P31 by slow neutron bombardment has been used as a methodof compensating p-type material to produce high resistivity silicon.20


A case which defies analysis is that of fission fragment damage.

The intense damage spike produced by the entry of highly charged heavy

particles and deposition in the lattice of radioactive nuclei is too

complicated a process to permit detailed understanding. However, in p-n

junction detectors, it is known that the damage tends to produce more

intrinsic material than was present before irradiation. This presumably

results from the production of donors and acceptors near the middle of

the band-gap of the material.

From these general considerations we conclude that the most important

types of damage to the nuclear spectrocopist, not concerned with heavy ion

or fission fragment research, are likely to be those due to fairly heavy

charged particles (such as protons or alpha particles) and to fast neutrons.

The cross section for fast neutron collisions is about 3 x 10-22 cm2

(corresponding to a mean free path of about 0.5 cm) and the energy distri-

bution of Si recoils is flat up to Emax where Emax is given by:

Emax = 0.133 En (4.15)

The average energy of the recoils is therefore half this value. The energy

of the silicon recoil atom is partly expended in producing ionization and

partly in producing secondary defects. As long as the silicon nucleus is

moving at high velocity it will be stripped of some of its atomic electrons

and therefore behave as a charged particle. As it slows down it will become

uncharged by capturing electrons. The threshold energy of an uncharged

silicon atom to produce ionization is 7 keV and therefore the minimum number

of defects per neutron collision (assuming ERECOIL > 7 keV) is 7000/Ed

where Ed is the energy required to displace a silicon atom.* This means

*Very little of the silicon atoms energy is likely to be lost to vibrationalmodes of the lattice as the wavelength equivalent of the silicon atom ismuch smaller than the lattice dimensions.


that each neutron collision produces a minimum of about 300 Frenkel pairs.

Depending upon the fraction of the primary silicon atom's recoil energy

used up in ionizing collisions before it slows down to the 7 keV level the

Emaxnumber of Frenkel pairs produced can range from 300 to about _ . If2 Ed

Emax = 1 MeV this upper limit is well over 1000 defects. It is likely

that most of the energy above 7 keV will be lost by ionizing collisions

and, for the moment, we will assume that 500 defects are produced per

fast neutron collision. 1010 neutrons/cm2 will then produce about 2 x 109

primary recoils in a 0.1 cm thick (1 cm2) slab of silicon and 1012 total

Frenkel defects will be produced in the material as a result of this

bombardment.

In the case of charged particles, such as alpha-particles, the mean

energy acquired by the primary silicon recoils is low but the number of

primary recoils is large. Dearnaley has analyzed this situation and Fig. 4.3

shows his results for alpha-particles and protons. Integration of the curve

to determine the total number of defects produced by a 40 MeV alpha-particle

shows that it leaves about 400 defects along its track. This means that

1010 such alpha-particles will leave about 4 x 1012 defects in a 0.1 cm

thick piece of silicon. This is about the same number as was calculated for

the fast neutron case but the defects have a different spatial distribution

in the material.

4.2.2 Consequences of Damage in p-n Junction Detectors

A confusing mass of literature exists on the results of radiation damage

to detectors. Most of the experimental data has been obtained under poorly

controlled conditions in which the measurement of damage was a secondary

objective in a nuclear experiment. Moreover the consequences of irradiation


depend on the type of detector and they may depend upon details of the

manufacturing process. To provide a logical interpretation of the results

some restrictions must be placed upon the scope of the following discussion.

In particular we will not discuss surface barrier detectors as the lack of

knowledge of the nature of the barrier makes it difficult to assess the

likely effect of radiation in the barrier itself. There is evidence that

the barrier is damaged by quite small doses of fission fragments ( ~ 107/cm2).

We will further restrict the discussion by eliminating consideration of any

deleterious effects produced by radiation in the surface layer at the edge

of the junction. There is evidence that surface properties can be affected

in certain radiation environments but the effects are complex and are quite

unimportant in the case of detectors used for spectroscopy.

These restrictions limit us to considering the coasequeaces of bulk

damage of the Frenkel defect type in silicon p-n junction and lithium drifted

silicon detectors. It is necessary to realize at the outset that the probable

consequences of damage to a detector are directly related to the ratio of the

number of active acceptor (or donor) atoms in the bulk to the number of

defects produced by the radiation. If few defects are produced compared with

the acceptor concentration,the effect of the damage on the detector properties

is likely to be small. A consequence of this is that p-n junction detectors -

particularly those made with low resistivity bulk material - are much less

prone to damage than lithium-drifted detectors. One might argue that this

is, in fact, a consequence of the thickness of the detector which is,

of course, related to the resistivity.


From Fig. 1.3 we see that the acceptor concentration in the bulk of

a detector made from 1000 ohm cm p-type silicon is about 2 x 1013 atoms/cm3.

We would therefore be surprised if a defect level close to this could not

be tolerated. According to Dearnaley's calculations this will correspond

to the damage produced by about 1011 alpha-particles (40 MeV), 1011 fast

neutrons, 5 x 1011 protons (10 MeV) or 1014 fast electrons. Here we are

assuming that each defect finally behaves as an acceptor or donor. In fact,

the effects of damage become evident at just about these doses. However,

the details of the damage process and its precise effect in detector

characteristics are not easy to explain. In one group of detectors21 made

from p-type bulk material the effect of electron irradiation was to increase

the bulk resistivity but the effect of proton irradiation was the reverse.

In the first case, the damage did not anneal out over a long period of time

but it did so to a big extent in the second case. Any explanation for these

results must postulate the formation of different sets of levels due to the

defects or due to their migration through the lattice. Pairing of vacancies

and oxygen atoms has been postulated as one factor in this process. Pre-

sumably the striking difference between the effects of electrons and protons

must be associated with the different densities of defects in the "spikes"

produced by the two types of particles. One is tempted to explain the

recovery effect in the proton case by a partial re-association of vacancies

and interstitials in the rather dense damage track. If this is so, a similar

recovery might be expected after alpha-particle or fast neutron damage. To

my knowledge, detailed measurements on this have not been reported.

The use of p-n junction detectors in fission physics research has been

one of the most important areas of application of detectors for several years.

It has therefore been important to consider ways to reduce the sensitivity of


these detectors to fission fragment damage. P-N junction detectors made

on high resistivity p-type material (e.g., 2000 ohm cm) show severe damage

effects after doses of 107 to 108 fragments/cm2. As we might expect,

reduction of the bulk resistivity to 400 ohm cm has increased the useful

range into the 108 to 109 fragments/cm2 range. Furthermore, Gibson22 has

reported excellent radiation damage behaviour in thin punched-through

detectors operated at voltages much larger than those required to deplete

the thickness of the wafer. This might be anticipated since the detector

would be expected to operate reasonably well until the donor* (or acceptor)

density introduced by the damage process was high enough to prevent the

punch-through condition.

Apart from the effect of damage on the bulk resistivity of the detector

material (which causes electric field changes), the levels introduced in

the forbidden gap provide recombination and generation centers. Consequently

the detector leakage current tends to increase and significant amounts of

charge may disappear during the charge collection process. Since these

effects may not be uniform in the whole sensitive volume of the detector,

worsening of energy resolution and the appearance of multiple peaks in the

amplitude spectrum are common signs of substantial radiation damage.

4.2.3 Consequences of Damage in Lithium-Drifted Silicon Detectors.

From the considerations outlined in the previous section it will be

obvious that these detectors are more sensitive to damage than the p-n

junction detectors. In our experience the worst effect of the damage is

to prevent total depletion of the detector thickness by the applied voltage.

There is evidence that fission fragment damage at least in p-type materialtends to make the material change in an n-type direction.


We will consider a 3 mm thick silicon detector with 300 V applied to it.

We can easily show that this will only just be depleted if 2 x 1010

acceptors/cm3 are introduced uniformly through the material. In 3 mm

thickness this means that about 1010 acceptors/cm2 are permissable. From

section 4.3.1, we can see that 1010 neutrons/cm2 produce about 3 x 1012

defects in 3 mm of silicon. Alternatively 1010 40 MeV alphas/cm2 produce

about the same number of defects. We might therefore expect signs of

damage* to occur at neutron or alpha doses of about 108/cm2. Results in

agreement with this conclusion have been reported by Mann and Yntema23.

Our own experimental observations on damage in lithium-drifted silicon

detetors induced during nuclear reaction experiments in the bombarding

particle energy range from 20 to 120 MeV are of’ interest in throwing some

light on the damage process. In summary these results are as follows:

(a) For practical purposes, damage in such scattering experiments

is almost entirely due to fast neutrons. These neutrons originate

at the target, collimating slits, and in the carbon absorber of

the Faraday-cup. Clear proof that damage is due to neutrons is

afforded by the observation that damage is not confined to the

region of the collimating slit image in the detector.

(b) The dominant consequence of the damage is the appearance of a

dead layer at the entry window of the detector. Increasing the

applied voltage can correct this up to the limit at which edge

breakdown causes substantial noise.

*It seems likely, and is experimentally observed, that the failure to depletethe material, with consequent appearance of a dead layer at the entry faceof the detector, is the most impor tant consequence of damage. Leakagecurrent and charge loss during collection are negligible.

Lecture 4 -158-

(c) After irradiation, the effects of the damage increase by a large

factor over a period of several weeks. We deduce from this that

the vacancies/interstitial pairs have very little direct effect

on the electrical behavior of the detector. However, migration

of the vacancies and lithium atoms may cause lithium precipitation

at the vacancies in due course. Thus, the donors are slowly

removed and the material becomes uncompensated. A consequence

of this is that detectors show no signs of damage during experi-

ments until they have received neutron doses much larger than

the 108/cm3 mentioned earlier.

(d) No increase in leakage due to either surface or bulk effects is

noted at the radiation levels at which the previously mentioned

effects occur.

(e) No shift of peaks in spectra is observed, nor does the energy

resolution change until the dead layer appears.

(f) In fast coincidence experiments a change in timing is the first

apparent effect of radiation damage. In a sensitive experiment

this can be observed for a total dose an order of magnitude

smaller than that at which any dead layer is seen. The change in

timing results from electric field lines terminating on radiation

produced acceptors thereby reducing the electric field in the region

toward the back of the detector.

While some workers have reported cases where the characteristics have

been recovered by redrifting the lithium, our results, if correctly inter-

preted, offer little hope of any substantial improvement in the radiation

sensitivity of lithium-driited detectors. Almost perfect material is required

for thick detectors and an unfortunate consequence of radiation damage is that


we no longer have adequate material. Repurification of the mateial and

recrystallization may well be the only solution to damage in this case.

ACKNOWLEDGEMENTS

Many people have contributed ideas and effort to these notes. In

particular, I should like to thank W. Hansen, R. Lothrop, M. Roach,

B. Jarrett, D. Landis, R. Pehl, and S. Antman for spending valuable

time discussing various aspects of the lectures. My thanks are also

due to several experimenters in the Nuclear Chemistry Department of the

Lawrence Radiation Laboratory for their stimulation and constant interest

in developing and using detectors. Without their active support little

of this work would have been possible. Finally thanks are due to

Leo Schifferle and Mary Thibideau for their constant help in preparing

the script and figures.

This work was carried out as part of the program of the Nuclear

Chemistry Instrumentation Group of the Lawrence Radiation Laboratory

supported by A.E.C. contract No. W-7405-eng-48.



Fig. 4.1 Collection of Hole-electron Pair in a p-i-n Detector

Fig. 4.2 Signal Output Due to a Single Electron Hole Pair in a p-i-n

Fig. 4.3 Collection of Hole-Electron Pair in a P-N-Junction

Fig. 4.4 Signal Output due to a Single Electron-Hole Pair in a P-N

Fig. 4.5 Expected Range of Pulse Shapes from p-i-n Germanium Detector at 77°K.

Fig. 4.6 Distribution in Triggering Delays of a Discriminator set to β-Peak

Pulse Amplitude from a Germanium Detector.

Fig. 4.7 Detector Pulse Shape for Alphas(Silicon Detector W = 3 mm,)

V = 350 V,

T = 25°C.

Fig. 4.8 Frenkel Defect Production by Alphas and Protons (Silicon)

(No Velocity Saturation Case)

Detector.

(No Velocity Saturation Case)

Junction Detector.

(Assuming V > 1000 Volts/cm)

(After Dearnaley)

-169- UCRL-16231

1. V. Fano, Phys. Rev. 70, 44 (1946).

2. V. Fano, Phys. Rev. 72, 26 (1947).

3. J. B. Birks, Theory and Practice of Scintillation Counting (Pergamon,

MacMillan, Co., New York, 1964) p. 662.

4. P. Iredale, Nuclear Inst. & Methods 11, 336 (1961).

5. P. Thieburger, et al., Proc. of Symposium on Nuclear Instruments,

Harwell, Sept., 1961 (Academic Press) p. 54.

6. W. Shockley, Proc. IRE 46, 973 (1958).

7. T. M. Buck, Semiconductor Nuclear Particle Detectors, N.R.C. Pub. #871,

p. 111 (1961).

8. F. S. Goulding, W. L. Hansen, N.R.C. Pub. #871, p. 202 (1961).

9. W. L. Hansen, F. S, Goulding, Nuclear Instr. & Methods 29, 345 (1964).

10. R. Deshpande, Solid State Electronics 8, 313 (1965).

11. H. Reiss, C. S. Fuller & F, J. Morin, Bell System Tech, Jour. XXXV,

535 (1956).

12. E. M. Pell, N.R.C. Pub. #871, p. 136 (1961).

13. W. L. Hansen, B. Jarrett, Nuclear Instr. & Methods 31, 301 (1964).

14. F. S. Goulding, W. L. Hansen, IEEE Trans. on Nucl. Sci. NS-11, 286 (1964).

15. A. J. Tavendale, IEEE Trans. on Nucl. Sci, NS-11, 191 (1964).

16. A. C. Prior, J. Chem. Phys, Solids 12, 175 (1960).

17. T. K. Alexander, et al., Phys. Rev. Letters 13, 86 (1964).

18. G. Dearnaley, D. C. Northrop, Semiconductor Counters for Nuclear

Radiations (John Wiley & Sons, Inc., New York, 1963).

19. (Not Used)

-170- UCRL-16231

20. J. Messier, et al., IEEE Trans. on Nucl. Sci. NS-11, 276 (1964).

21. R. E. Scott, IEEE Trans. on Nucl. Sci. NS-11, 206 (1964).

22. W. M. Gibson, Private Communication.

23. H. M. Mann & J. L. Yntema, IEEE Trans. on Nucl. Sci. NS-11, 201 (1964).

24. W. Van Hoosbroeck, Private Communication.

25. A. Van der Ziel, Proc. IRE 50, 1808 (1962).

26. A. Van der Ziel, Proc. IRE 51, 461 (1963).

27. O. Meyer, Nuclear Instr. & Methods 33, 164 (1965).

28. T. W. Nybakken, V. Vali, Nuclear Instr. & Methods 32, 121 (1965).

Documents

UCRL-16231 UNIVERSITY OF CALIFORNIA AEC …TO: FROM: Subject: UNIVERSITY OF CALIFORNIA Lawrence Radiation Laboratory Berkeley, California AEC Contract No. W-7405-eng-48 September 24,